# HG changeset patch # User haftmann # Date 1244644044 -7200 # Node ID 2b47e8e37c1107fbeafd9e4fb7a9301488ab0f0c # Parent 8d353e3214d0bf7300225032f21ed2398dc3a7c5 separate directory for datatype package diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_abs_proofs.ML --- a/src/HOL/Tools/datatype_abs_proofs.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,446 +0,0 @@ -(* Title: HOL/Tools/datatype_abs_proofs.ML - Author: Stefan Berghofer, TU Muenchen - -Proofs and defintions independent of concrete representation -of datatypes (i.e. requiring only abstract properties such as -injectivity / distinctness of constructors and induction) - - - case distinction (exhaustion) theorems - - characteristic equations for primrec combinators - - characteristic equations for case combinators - - equations for splitting "P (case ...)" expressions - - "nchotomy" and "case_cong" theorems for TFL -*) - -signature DATATYPE_ABS_PROOFS = -sig - val prove_casedist_thms : string list -> - DatatypeAux.descr list -> (string * sort) list -> thm -> - attribute list -> theory -> thm list * theory - val prove_primrec_thms : bool -> string list -> - DatatypeAux.descr list -> (string * sort) list -> - DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list -> - simpset -> thm -> theory -> (string list * thm list) * theory - val prove_case_thms : bool -> string list -> - DatatypeAux.descr list -> (string * sort) list -> - string list -> thm list -> theory -> (thm list list * string list) * theory - val prove_split_thms : string list -> - DatatypeAux.descr list -> (string * sort) list -> - thm list list -> thm list list -> thm list -> thm list list -> theory -> - (thm * thm) list * theory - val prove_nchotomys : string list -> DatatypeAux.descr list -> - (string * sort) list -> thm list -> theory -> thm list * theory - val prove_weak_case_congs : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> thm list * theory - val prove_case_congs : string list -> - DatatypeAux.descr list -> (string * sort) list -> - thm list -> thm list list -> theory -> thm list * theory -end; - -structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS = -struct - -open DatatypeAux; - -(************************ case distinction theorems ***************************) - -fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy = - let - val _ = message "Proving case distinction theorems ..."; - - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - - val {maxidx, ...} = rep_thm induct; - val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); - - fun prove_casedist_thm ((i, t), T) = - let - val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => - Abs ("z", T', Const ("True", T''))) induct_Ps; - val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $ - Var (("P", 0), HOLogic.boolT)) - val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs))); - val cert = cterm_of thy; - val insts' = (map cert induct_Ps) ~~ (map cert insts); - val induct' = refl RS ((List.nth - (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp)) - - in - SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) - (fn {prems, ...} => EVERY - [rtac induct' 1, - REPEAT (rtac TrueI 1), - REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), - REPEAT (rtac TrueI 1)]) - end; - - val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~ - (DatatypeProp.make_casedists descr sorts) ~~ newTs) - in - thy - |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms - end; - - -(*************************** primrec combinators ******************************) - -fun prove_primrec_thms flat_names new_type_names descr sorts - (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy = - let - val _ = message "Constructing primrec combinators ..."; - - val big_name = space_implode "_" new_type_names; - val thy0 = add_path flat_names big_name thy; - - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; - val newTs = Library.take (length (hd descr), recTs); - - val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); - - val big_rec_name' = big_name ^ "_rec_set"; - val rec_set_names' = - if length descr' = 1 then [big_rec_name'] else - map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int) - (1 upto (length descr')); - val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; - - val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used; - - val rec_set_Ts = map (fn (T1, T2) => - reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); - - val rec_fns = map (uncurry (mk_Free "f")) - (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); - val rec_sets' = map (fn c => list_comb (Free c, rec_fns)) - (rec_set_names' ~~ rec_set_Ts); - val rec_sets = map (fn c => list_comb (Const c, rec_fns)) - (rec_set_names ~~ rec_set_Ts); - - (* introduction rules for graph of primrec function *) - - fun make_rec_intr T rec_set ((rec_intr_ts, l), (cname, cargs)) = - let - fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) = - let val free1 = mk_Free "x" U j - in (case (strip_dtyp dt, strip_type U) of - ((_, DtRec m), (Us, _)) => - let - val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k; - val i = length Us - in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all - (map (pair "x") Us, List.nth (rec_sets', m) $ - app_bnds free1 i $ app_bnds free2 i)) :: prems, - free1::t1s, free2::t2s) - end - | _ => (j + 1, k, prems, free1::t1s, t2s)) - end; - - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val (_, _, prems, t1s, t2s) = List.foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts) - - in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop - (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ - list_comb (List.nth (rec_fns, l), t1s @ t2s)))], l + 1) - end; - - val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) => - Library.foldl (make_rec_intr T set_name) (x, #3 (snd d))) - (([], 0), descr' ~~ recTs ~~ rec_sets'); - - val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = - InductivePackage.add_inductive_global (serial_string ()) - {quiet_mode = ! quiet_mode, verbose = false, kind = Thm.internalK, - alt_name = Binding.name big_rec_name', coind = false, no_elim = false, no_ind = true, - skip_mono = true, fork_mono = false} - (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) - (map dest_Free rec_fns) - (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] thy0; - - (* prove uniqueness and termination of primrec combinators *) - - val _ = message "Proving termination and uniqueness of primrec functions ..."; - - fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) = - let - val distinct_tac = - (if i < length newTs then - full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1 - else full_simp_tac dist_ss 1); - - val inject = map (fn r => r RS iffD1) - (if i < length newTs then List.nth (constr_inject, i) - else #inject (the (Symtab.lookup dt_info tname))); - - fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) = - let - val k = length (List.filter is_rec_type cargs) - - in (EVERY [DETERM tac, - REPEAT (etac ex1E 1), rtac ex1I 1, - DEPTH_SOLVE_1 (ares_tac [intr] 1), - REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1), - etac elim 1, - REPEAT_DETERM_N j distinct_tac, - TRY (dresolve_tac inject 1), - REPEAT (etac conjE 1), hyp_subst_tac 1, - REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), - TRY (hyp_subst_tac 1), - rtac refl 1, - REPEAT_DETERM_N (n - j - 1) distinct_tac], - intrs, j + 1) - end; - - val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs)) - ((tac, intrs, 0), constrs); - - in (tac', intrs') end; - - val rec_unique_thms = - let - val rec_unique_ts = map (fn (((set_t, T1), T2), i) => - Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ - absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2))) - (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); - val cert = cterm_of thy1 - val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t)) - ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); - val induct' = cterm_instantiate ((map cert induct_Ps) ~~ - (map cert insts)) induct; - val (tac, _) = Library.foldl mk_unique_tac - (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1 - THEN rewrite_goals_tac [mk_meta_eq choice_eq], rec_intrs), - descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts); - - in split_conj_thm (SkipProof.prove_global thy1 [] [] - (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)) - end; - - val rec_total_thms = map (fn r => r RS theI') rec_unique_thms; - - (* define primrec combinators *) - - val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; - val reccomb_names = map (Sign.full_bname thy1) - (if length descr' = 1 then [big_reccomb_name] else - (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) - (1 upto (length descr')))); - val reccombs = map (fn ((name, T), T') => list_comb - (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) - (reccomb_names ~~ recTs ~~ rec_result_Ts); - - val (reccomb_defs, thy2) = - thy1 - |> Sign.add_consts_i (map (fn ((name, T), T') => - (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) - (reccomb_names ~~ recTs ~~ rec_result_Ts)) - |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => - (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T, - Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T', - set $ Free ("x", T) $ Free ("y", T')))))) - (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) - ||> parent_path flat_names - ||> Theory.checkpoint; - - - (* prove characteristic equations for primrec combinators *) - - val _ = message "Proving characteristic theorems for primrec combinators ..." - - val rec_thms = map (fn t => SkipProof.prove_global thy2 [] [] t - (fn _ => EVERY - [rewrite_goals_tac reccomb_defs, - rtac the1_equality 1, - resolve_tac rec_unique_thms 1, - resolve_tac rec_intrs 1, - REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) - (DatatypeProp.make_primrecs new_type_names descr sorts thy2) - - in - thy2 - |> Sign.add_path (space_implode "_" new_type_names) - |> PureThy.add_thmss [((Binding.name "recs", rec_thms), - [Nitpick_Const_Simp_Thms.add])] - ||> Sign.parent_path - ||> Theory.checkpoint - |-> (fn thms => pair (reccomb_names, Library.flat thms)) - end; - - -(***************************** case combinators *******************************) - -fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy = - let - val _ = message "Proving characteristic theorems for case combinators ..."; - - val thy1 = add_path flat_names (space_implode "_" new_type_names) thy; - - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; - val newTs = Library.take (length (hd descr), recTs); - val T' = TFree (Name.variant used "'t", HOLogic.typeS); - - fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T'; - - val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val Ts' = map mk_dummyT (List.filter is_rec_type cargs) - in Const (@{const_name undefined}, Ts @ Ts' ---> T') - end) constrs) descr'; - - val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names; - - (* define case combinators via primrec combinators *) - - val (case_defs, thy2) = Library.foldl (fn ((defs, thy), - ((((i, (_, _, constrs)), T), name), recname)) => - let - val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) => - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs); - val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts')); - val frees = Library.take (length cargs, frees'); - val free = mk_Free "f" (Ts ---> T') j - in - (free, list_abs_free (map dest_Free frees', - list_comb (free, frees))) - end) (constrs ~~ (1 upto length constrs))); - - val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T'; - val fns = (List.concat (Library.take (i, case_dummy_fns))) @ - fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))); - val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); - val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); - val def = (Binding.name (Long_Name.base_name name ^ "_def"), - Logic.mk_equals (list_comb (Const (name, caseT), fns1), - list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @ - fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) ))); - val ([def_thm], thy') = - thy - |> Sign.declare_const [] decl |> snd - |> (PureThy.add_defs false o map Thm.no_attributes) [def]; - - in (defs @ [def_thm], thy') - end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~ - (Library.take (length newTs, reccomb_names))) - ||> Theory.checkpoint; - - val case_thms = map (map (fn t => SkipProof.prove_global thy2 [] [] t - (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))) - (DatatypeProp.make_cases new_type_names descr sorts thy2) - in - thy2 - |> Context.the_theory o fold (fold Nitpick_Const_Simp_Thms.add_thm) case_thms - o Context.Theory - |> parent_path flat_names - |> store_thmss "cases" new_type_names case_thms - |-> (fn thmss => pair (thmss, case_names)) - end; - - -(******************************* case splitting *******************************) - -fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites - casedist_thms case_thms thy = - let - val _ = message "Proving equations for case splitting ..."; - - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - - fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), - exhaustion), case_thms'), T) = - let - val cert = cterm_of thy; - val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); - val exhaustion' = cterm_instantiate - [(cert lhs, cert (Free ("x", T)))] exhaustion; - val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac - (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]) - in - (SkipProof.prove_global thy [] [] t1 tacf, - SkipProof.prove_global thy [] [] t2 tacf) - end; - - val split_thm_pairs = map prove_split_thms - ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~ - dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); - - val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs - - in - thy - |> store_thms "split" new_type_names split_thms - ||>> store_thms "split_asm" new_type_names split_asm_thms - |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) - end; - -fun prove_weak_case_congs new_type_names descr sorts thy = - let - fun prove_weak_case_cong t = - SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) - (fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1]) - - val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs - new_type_names descr sorts thy) - - in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end; - -(************************* additional theorems for TFL ************************) - -fun prove_nchotomys new_type_names descr sorts casedist_thms thy = - let - val _ = message "Proving additional theorems for TFL ..."; - - fun prove_nchotomy (t, exhaustion) = - let - (* For goal i, select the correct disjunct to attack, then prove it *) - fun tac i 0 = EVERY [TRY (rtac disjI1 i), - hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i] - | tac i n = rtac disjI2 i THEN tac i (n - 1) - in - SkipProof.prove_global thy [] [] t (fn _ => - EVERY [rtac allI 1, - exh_tac (K exhaustion) 1, - ALLGOALS (fn i => tac i (i-1))]) - end; - - val nchotomys = - map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms) - - in thy |> store_thms "nchotomy" new_type_names nchotomys end; - -fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy = - let - fun prove_case_cong ((t, nchotomy), case_rewrites) = - let - val (Const ("==>", _) $ tm $ _) = t; - val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm; - val cert = cterm_of thy; - val nchotomy' = nchotomy RS spec; - val [v] = Term.add_vars (concl_of nchotomy') []; - val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy' - in - SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) - (fn {prems, ...} => - let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites)) - in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1, - cut_facts_tac [nchotomy''] 1, - REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), - REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] - end) - end; - - val case_congs = map prove_case_cong (DatatypeProp.make_case_congs - new_type_names descr sorts thy ~~ nchotomys ~~ case_thms) - - in thy |> store_thms "case_cong" new_type_names case_congs end; - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_aux.ML --- a/src/HOL/Tools/datatype_aux.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,348 +0,0 @@ -(* Title: HOL/Tools/datatype_aux.ML - Author: Stefan Berghofer, TU Muenchen - -Auxiliary functions for defining datatypes. -*) - -signature DATATYPE_AUX = -sig - val quiet_mode : bool ref - val message : string -> unit - - val add_path : bool -> string -> theory -> theory - val parent_path : bool -> theory -> theory - - val store_thmss_atts : string -> string list -> attribute list list -> thm list list - -> theory -> thm list list * theory - val store_thmss : string -> string list -> thm list list -> theory -> thm list list * theory - val store_thms_atts : string -> string list -> attribute list list -> thm list - -> theory -> thm list * theory - val store_thms : string -> string list -> thm list -> theory -> thm list * theory - - val split_conj_thm : thm -> thm list - val mk_conj : term list -> term - val mk_disj : term list -> term - - val app_bnds : term -> int -> term - - val cong_tac : int -> tactic - val indtac : thm -> string list -> int -> tactic - val exh_tac : (string -> thm) -> int -> tactic - - datatype simproc_dist = FewConstrs of thm list - | ManyConstrs of thm * simpset; - - datatype dtyp = - DtTFree of string - | DtType of string * (dtyp list) - | DtRec of int; - type descr - type datatype_info - - exception Datatype - exception Datatype_Empty of string - val name_of_typ : typ -> string - val dtyp_of_typ : (string * string list) list -> typ -> dtyp - val mk_Free : string -> typ -> int -> term - val is_rec_type : dtyp -> bool - val typ_of_dtyp : descr -> (string * sort) list -> dtyp -> typ - val dest_DtTFree : dtyp -> string - val dest_DtRec : dtyp -> int - val strip_dtyp : dtyp -> dtyp list * dtyp - val body_index : dtyp -> int - val mk_fun_dtyp : dtyp list -> dtyp -> dtyp - val get_nonrec_types : descr -> (string * sort) list -> typ list - val get_branching_types : descr -> (string * sort) list -> typ list - val get_arities : descr -> int list - val get_rec_types : descr -> (string * sort) list -> typ list - val check_nonempty : descr list -> unit - val unfold_datatypes : - theory -> descr -> (string * sort) list -> datatype_info Symtab.table -> - descr -> int -> descr list * int -end; - -structure DatatypeAux : DATATYPE_AUX = -struct - -val quiet_mode = ref false; -fun message s = if !quiet_mode then () else writeln s; - -fun add_path flat_names s = if flat_names then I else Sign.add_path s; -fun parent_path flat_names = if flat_names then I else Sign.parent_path; - - -(* store theorems in theory *) - -fun store_thmss_atts label tnames attss thmss = - fold_map (fn ((tname, atts), thms) => - Sign.add_path tname - #> PureThy.add_thmss [((Binding.name label, thms), atts)] - #-> (fn thm::_ => Sign.parent_path #> pair thm)) (tnames ~~ attss ~~ thmss) - ##> Theory.checkpoint; - -fun store_thmss label tnames = store_thmss_atts label tnames (replicate (length tnames) []); - -fun store_thms_atts label tnames attss thmss = - fold_map (fn ((tname, atts), thms) => - Sign.add_path tname - #> PureThy.add_thms [((Binding.name label, thms), atts)] - #-> (fn thm::_ => Sign.parent_path #> pair thm)) (tnames ~~ attss ~~ thmss) - ##> Theory.checkpoint; - -fun store_thms label tnames = store_thms_atts label tnames (replicate (length tnames) []); - - -(* split theorem thm_1 & ... & thm_n into n theorems *) - -fun split_conj_thm th = - ((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th]; - -val mk_conj = foldr1 (HOLogic.mk_binop "op &"); -val mk_disj = foldr1 (HOLogic.mk_binop "op |"); - -fun app_bnds t i = list_comb (t, map Bound (i - 1 downto 0)); - - -fun cong_tac i st = (case Logic.strip_assums_concl - (List.nth (prems_of st, i - 1)) of - _ $ (_ $ (f $ x) $ (g $ y)) => - let - val cong' = Thm.lift_rule (Thm.cprem_of st i) cong; - val _ $ (_ $ (f' $ x') $ (g' $ y')) = - Logic.strip_assums_concl (prop_of cong'); - val insts = map (pairself (cterm_of (Thm.theory_of_thm st)) o - apsnd (curry list_abs (Logic.strip_params (concl_of cong'))) o - apfst head_of) [(f', f), (g', g), (x', x), (y', y)] - in compose_tac (false, cterm_instantiate insts cong', 2) i st - handle THM _ => no_tac st - end - | _ => no_tac st); - -(* instantiate induction rule *) - -fun indtac indrule indnames i st = - let - val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule)); - val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop - (Logic.strip_imp_concl (List.nth (prems_of st, i - 1)))); - val getP = if can HOLogic.dest_imp (hd ts) then - (apfst SOME) o HOLogic.dest_imp else pair NONE; - val flt = if null indnames then I else - filter (fn Free (s, _) => s mem indnames | _ => false); - fun abstr (t1, t2) = (case t1 of - NONE => (case flt (OldTerm.term_frees t2) of - [Free (s, T)] => SOME (absfree (s, T, t2)) - | _ => NONE) - | SOME (_ $ t') => SOME (Abs ("x", fastype_of t', abstract_over (t', t2)))) - val cert = cterm_of (Thm.theory_of_thm st); - val insts = List.mapPartial (fn (t, u) => case abstr (getP u) of - NONE => NONE - | SOME u' => SOME (t |> getP |> snd |> head_of |> cert, cert u')) (ts ~~ ts'); - val indrule' = cterm_instantiate insts indrule - in - rtac indrule' i st - end; - -(* perform exhaustive case analysis on last parameter of subgoal i *) - -fun exh_tac exh_thm_of i state = - let - val thy = Thm.theory_of_thm state; - val prem = nth (prems_of state) (i - 1); - val params = Logic.strip_params prem; - val (_, Type (tname, _)) = hd (rev params); - val exhaustion = Thm.lift_rule (Thm.cprem_of state i) (exh_thm_of tname); - val prem' = hd (prems_of exhaustion); - val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem')); - val exhaustion' = cterm_instantiate [(cterm_of thy (head_of lhs), - cterm_of thy (List.foldr (fn ((_, T), t) => Abs ("z", T, t)) - (Bound 0) params))] exhaustion - in compose_tac (false, exhaustion', nprems_of exhaustion) i state - end; - -(* handling of distinctness theorems *) - -datatype simproc_dist = FewConstrs of thm list - | ManyConstrs of thm * simpset; - -(********************** Internal description of datatypes *********************) - -datatype dtyp = - DtTFree of string - | DtType of string * (dtyp list) - | DtRec of int; - -(* information about datatypes *) - -(* index, datatype name, type arguments, constructor name, types of constructor's arguments *) -type descr = (int * (string * dtyp list * (string * dtyp list) list)) list; - -type datatype_info = - {index : int, - alt_names : string list option, - descr : descr, - sorts : (string * sort) list, - rec_names : string list, - rec_rewrites : thm list, - case_name : string, - case_rewrites : thm list, - induction : thm, - exhaustion : thm, - distinct : simproc_dist, - inject : thm list, - nchotomy : thm, - case_cong : thm, - weak_case_cong : thm}; - -fun mk_Free s T i = Free (s ^ (string_of_int i), T); - -fun subst_DtTFree _ substs (T as (DtTFree name)) = - AList.lookup (op =) substs name |> the_default T - | subst_DtTFree i substs (DtType (name, ts)) = - DtType (name, map (subst_DtTFree i substs) ts) - | subst_DtTFree i _ (DtRec j) = DtRec (i + j); - -exception Datatype; -exception Datatype_Empty of string; - -fun dest_DtTFree (DtTFree a) = a - | dest_DtTFree _ = raise Datatype; - -fun dest_DtRec (DtRec i) = i - | dest_DtRec _ = raise Datatype; - -fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts - | is_rec_type (DtRec _) = true - | is_rec_type _ = false; - -fun strip_dtyp (DtType ("fun", [T, U])) = apfst (cons T) (strip_dtyp U) - | strip_dtyp T = ([], T); - -val body_index = dest_DtRec o snd o strip_dtyp; - -fun mk_fun_dtyp [] U = U - | mk_fun_dtyp (T :: Ts) U = DtType ("fun", [T, mk_fun_dtyp Ts U]); - -fun name_of_typ (Type (s, Ts)) = - let val s' = Long_Name.base_name s - in space_implode "_" (List.filter (not o equal "") (map name_of_typ Ts) @ - [if Syntax.is_identifier s' then s' else "x"]) - end - | name_of_typ _ = ""; - -fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n - | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)" - | dtyp_of_typ new_dts (Type (tname, Ts)) = - (case AList.lookup (op =) new_dts tname of - NONE => DtType (tname, map (dtyp_of_typ new_dts) Ts) - | SOME vs => if map (try (fst o dest_TFree)) Ts = map SOME vs then - DtRec (find_index (curry op = tname o fst) new_dts) - else error ("Illegal occurrence of recursive type " ^ tname)); - -fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, (the o AList.lookup (op =) sorts) a) - | typ_of_dtyp descr sorts (DtRec i) = - let val (s, ds, _) = (the o AList.lookup (op =) descr) i - in Type (s, map (typ_of_dtyp descr sorts) ds) end - | typ_of_dtyp descr sorts (DtType (s, ds)) = - Type (s, map (typ_of_dtyp descr sorts) ds); - -(* find all non-recursive types in datatype description *) - -fun get_nonrec_types descr sorts = - map (typ_of_dtyp descr sorts) (Library.foldl (fn (Ts, (_, (_, _, constrs))) => - Library.foldl (fn (Ts', (_, cargs)) => - filter_out is_rec_type cargs union Ts') (Ts, constrs)) ([], descr)); - -(* get all recursive types in datatype description *) - -fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) => - Type (s, map (typ_of_dtyp descr sorts) ds)) descr; - -(* get all branching types *) - -fun get_branching_types descr sorts = - map (typ_of_dtyp descr sorts) (fold (fn (_, (_, _, constrs)) => - fold (fn (_, cargs) => fold (strip_dtyp #> fst #> fold (insert op =)) cargs) - constrs) descr []); - -fun get_arities descr = fold (fn (_, (_, _, constrs)) => - fold (fn (_, cargs) => fold (insert op =) (map (length o fst o strip_dtyp) - (List.filter is_rec_type cargs))) constrs) descr []; - -(* nonemptiness check for datatypes *) - -fun check_nonempty descr = - let - val descr' = List.concat descr; - fun is_nonempty_dt is i = - let - val (_, _, constrs) = (the o AList.lookup (op =) descr') i; - fun arg_nonempty (_, DtRec i) = if i mem is then false - else is_nonempty_dt (i::is) i - | arg_nonempty _ = true; - in exists ((forall (arg_nonempty o strip_dtyp)) o snd) constrs - end - in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr) - (fn (_, (s, _, _)) => raise Datatype_Empty s) - end; - -(* unfold a list of mutually recursive datatype specifications *) -(* all types of the form DtType (dt_name, [..., DtRec _, ...]) *) -(* need to be unfolded *) - -fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i = - let - fun typ_error T msg = error ("Non-admissible type expression\n" ^ - Syntax.string_of_typ_global sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg); - - fun get_dt_descr T i tname dts = - (case Symtab.lookup dt_info tname of - NONE => typ_error T (tname ^ " is not a datatype - can't use it in\ - \ nested recursion") - | (SOME {index, descr, ...}) => - let val (_, vars, _) = (the o AList.lookup (op =) descr) index; - val subst = ((map dest_DtTFree vars) ~~ dts) handle Library.UnequalLengths => - typ_error T ("Type constructor " ^ tname ^ " used with wrong\ - \ number of arguments") - in (i + index, map (fn (j, (tn, args, cs)) => (i + j, - (tn, map (subst_DtTFree i subst) args, - map (apsnd (map (subst_DtTFree i subst))) cs))) descr) - end); - - (* unfold a single constructor argument *) - - fun unfold_arg ((i, Ts, descrs), T) = - if is_rec_type T then - let val (Us, U) = strip_dtyp T - in if exists is_rec_type Us then - typ_error T "Non-strictly positive recursive occurrence of type" - else (case U of - DtType (tname, dts) => - let - val (index, descr) = get_dt_descr T i tname dts; - val (descr', i') = unfold_datatypes sign orig_descr sorts - dt_info descr (i + length descr) - in (i', Ts @ [mk_fun_dtyp Us (DtRec index)], descrs @ descr') end - | _ => (i, Ts @ [T], descrs)) - end - else (i, Ts @ [T], descrs); - - (* unfold a constructor *) - - fun unfold_constr ((i, constrs, descrs), (cname, cargs)) = - let val (i', cargs', descrs') = Library.foldl unfold_arg ((i, [], descrs), cargs) - in (i', constrs @ [(cname, cargs')], descrs') end; - - (* unfold a single datatype *) - - fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) = - let val (i', constrs', descrs') = - Library.foldl unfold_constr ((i, [], descrs), constrs) - in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs') - end; - - val (i', descr', descrs) = Library.foldl unfold_datatype ((i, [],[]), descr); - - in (descr' :: descrs, i') end; - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_case.ML --- a/src/HOL/Tools/datatype_case.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,469 +0,0 @@ -(* Title: HOL/Tools/datatype_case.ML - Author: Konrad Slind, Cambridge University Computer Laboratory - Author: Stefan Berghofer, TU Muenchen - -Nested case expressions on datatypes. -*) - -signature DATATYPE_CASE = -sig - val make_case: (string -> DatatypeAux.datatype_info option) -> - Proof.context -> bool -> string list -> term -> (term * term) list -> - term * (term * (int * bool)) list - val dest_case: (string -> DatatypeAux.datatype_info option) -> bool -> - string list -> term -> (term * (term * term) list) option - val strip_case: (string -> DatatypeAux.datatype_info option) -> bool -> - term -> (term * (term * term) list) option - val case_tr: bool -> (theory -> string -> DatatypeAux.datatype_info option) - -> Proof.context -> term list -> term - val case_tr': (theory -> string -> DatatypeAux.datatype_info option) -> - string -> Proof.context -> term list -> term -end; - -structure DatatypeCase : DATATYPE_CASE = -struct - -exception CASE_ERROR of string * int; - -fun match_type thy pat ob = Sign.typ_match thy (pat, ob) Vartab.empty; - -(*--------------------------------------------------------------------------- - * Get information about datatypes - *---------------------------------------------------------------------------*) - -fun ty_info (tab : string -> DatatypeAux.datatype_info option) s = - case tab s of - SOME {descr, case_name, index, sorts, ...} => - let - val (_, (tname, dts, constrs)) = nth descr index; - val mk_ty = DatatypeAux.typ_of_dtyp descr sorts; - val T = Type (tname, map mk_ty dts) - in - SOME {case_name = case_name, - constructors = map (fn (cname, dts') => - Const (cname, Logic.varifyT (map mk_ty dts' ---> T))) constrs} - end - | NONE => NONE; - - -(*--------------------------------------------------------------------------- - * Each pattern carries with it a tag (i,b) where - * i is the clause it came from and - * b=true indicates that clause was given by the user - * (or is an instantiation of a user supplied pattern) - * b=false --> i = ~1 - *---------------------------------------------------------------------------*) - -fun pattern_subst theta (tm, x) = (subst_free theta tm, x); - -fun row_of_pat x = fst (snd x); - -fun add_row_used ((prfx, pats), (tm, tag)) = - fold Term.add_free_names (tm :: pats @ prfx); - -(* try to preserve names given by user *) -fun default_names names ts = - map (fn ("", Free (name', _)) => name' | (name, _) => name) (names ~~ ts); - -fun strip_constraints (Const ("_constrain", _) $ t $ tT) = - strip_constraints t ||> cons tT - | strip_constraints t = (t, []); - -fun mk_fun_constrain tT t = Syntax.const "_constrain" $ t $ - (Syntax.free "fun" $ tT $ Syntax.free "dummy"); - - -(*--------------------------------------------------------------------------- - * Produce an instance of a constructor, plus genvars for its arguments. - *---------------------------------------------------------------------------*) -fun fresh_constr ty_match ty_inst colty used c = - let - val (_, Ty) = dest_Const c - val Ts = binder_types Ty; - val names = Name.variant_list used - (DatatypeProp.make_tnames (map Logic.unvarifyT Ts)); - val ty = body_type Ty; - val ty_theta = ty_match ty colty handle Type.TYPE_MATCH => - raise CASE_ERROR ("type mismatch", ~1) - val c' = ty_inst ty_theta c - val gvars = map (ty_inst ty_theta o Free) (names ~~ Ts) - in (c', gvars) - end; - - -(*--------------------------------------------------------------------------- - * Goes through a list of rows and picks out the ones beginning with a - * pattern with constructor = name. - *---------------------------------------------------------------------------*) -fun mk_group (name, T) rows = - let val k = length (binder_types T) - in fold (fn (row as ((prfx, p :: rst), rhs as (_, (i, _)))) => - fn ((in_group, not_in_group), (names, cnstrts)) => (case strip_comb p of - (Const (name', _), args) => - if name = name' then - if length args = k then - let val (args', cnstrts') = split_list (map strip_constraints args) - in - ((((prfx, args' @ rst), rhs) :: in_group, not_in_group), - (default_names names args', map2 append cnstrts cnstrts')) - end - else raise CASE_ERROR - ("Wrong number of arguments for constructor " ^ name, i) - else ((in_group, row :: not_in_group), (names, cnstrts)) - | _ => raise CASE_ERROR ("Not a constructor pattern", i))) - rows (([], []), (replicate k "", replicate k [])) |>> pairself rev - end; - -(*--------------------------------------------------------------------------- - * Partition the rows. Not efficient: we should use hashing. - *---------------------------------------------------------------------------*) -fun partition _ _ _ _ _ _ _ [] = raise CASE_ERROR ("partition: no rows", ~1) - | partition ty_match ty_inst type_of used constructors colty res_ty - (rows as (((prfx, _ :: rstp), _) :: _)) = - let - fun part {constrs = [], rows = [], A} = rev A - | part {constrs = [], rows = (_, (_, (i, _))) :: _, A} = - raise CASE_ERROR ("Not a constructor pattern", i) - | part {constrs = c :: crst, rows, A} = - let - val ((in_group, not_in_group), (names, cnstrts)) = - mk_group (dest_Const c) rows; - val used' = fold add_row_used in_group used; - val (c', gvars) = fresh_constr ty_match ty_inst colty used' c; - val in_group' = - if null in_group (* Constructor not given *) - then - let - val Ts = map type_of rstp; - val xs = Name.variant_list - (fold Term.add_free_names gvars used') - (replicate (length rstp) "x") - in - [((prfx, gvars @ map Free (xs ~~ Ts)), - (Const ("HOL.undefined", res_ty), (~1, false)))] - end - else in_group - in - part{constrs = crst, - rows = not_in_group, - A = {constructor = c', - new_formals = gvars, - names = names, - constraints = cnstrts, - group = in_group'} :: A} - end - in part {constrs = constructors, rows = rows, A = []} - end; - -(*--------------------------------------------------------------------------- - * Misc. routines used in mk_case - *---------------------------------------------------------------------------*) - -fun mk_pat ((c, c'), l) = - let - val L = length (binder_types (fastype_of c)) - fun build (prfx, tag, plist) = - let val (args, plist') = chop L plist - in (prfx, tag, list_comb (c', args) :: plist') end - in map build l end; - -fun v_to_prfx (prfx, v::pats) = (v::prfx,pats) - | v_to_prfx _ = raise CASE_ERROR ("mk_case: v_to_prfx", ~1); - -fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats) - | v_to_pats _ = raise CASE_ERROR ("mk_case: v_to_pats", ~1); - - -(*---------------------------------------------------------------------------- - * Translation of pattern terms into nested case expressions. - * - * This performs the translation and also builds the full set of patterns. - * Thus it supports the construction of induction theorems even when an - * incomplete set of patterns is given. - *---------------------------------------------------------------------------*) - -fun mk_case tab ctxt ty_match ty_inst type_of used range_ty = - let - val name = Name.variant used "a"; - fun expand constructors used ty ((_, []), _) = - raise CASE_ERROR ("mk_case: expand_var_row", ~1) - | expand constructors used ty (row as ((prfx, p :: rst), rhs)) = - if is_Free p then - let - val used' = add_row_used row used; - fun expnd c = - let val capp = - list_comb (fresh_constr ty_match ty_inst ty used' c) - in ((prfx, capp :: rst), pattern_subst [(p, capp)] rhs) - end - in map expnd constructors end - else [row] - fun mk {rows = [], ...} = raise CASE_ERROR ("no rows", ~1) - | mk {path = [], rows = ((prfx, []), (tm, tag)) :: _} = (* Done *) - ([(prfx, tag, [])], tm) - | mk {path, rows as ((row as ((_, [Free _]), _)) :: _ :: _)} = - mk {path = path, rows = [row]} - | mk {path = u :: rstp, rows as ((_, _ :: _), _) :: _} = - let val col0 = map (fn ((_, p :: _), (_, (i, _))) => (p, i)) rows - in case Option.map (apfst head_of) - (find_first (not o is_Free o fst) col0) of - NONE => - let - val rows' = map (fn ((v, _), row) => row ||> - pattern_subst [(v, u)] |>> v_to_prfx) (col0 ~~ rows); - val (pref_patl, tm) = mk {path = rstp, rows = rows'} - in (map v_to_pats pref_patl, tm) end - | SOME (Const (cname, cT), i) => (case ty_info tab cname of - NONE => raise CASE_ERROR ("Not a datatype constructor: " ^ cname, i) - | SOME {case_name, constructors} => - let - val pty = body_type cT; - val used' = fold Term.add_free_names rstp used; - val nrows = maps (expand constructors used' pty) rows; - val subproblems = partition ty_match ty_inst type_of used' - constructors pty range_ty nrows; - val new_formals = map #new_formals subproblems - val constructors' = map #constructor subproblems - val news = map (fn {new_formals, group, ...} => - {path = new_formals @ rstp, rows = group}) subproblems; - val (pat_rect, dtrees) = split_list (map mk news); - val case_functions = map2 - (fn {new_formals, names, constraints, ...} => - fold_rev (fn ((x as Free (_, T), s), cnstrts) => fn t => - Abs (if s = "" then name else s, T, - abstract_over (x, t)) |> - fold mk_fun_constrain cnstrts) - (new_formals ~~ names ~~ constraints)) - subproblems dtrees; - val types = map type_of (case_functions @ [u]); - val case_const = Const (case_name, types ---> range_ty) - val tree = list_comb (case_const, case_functions @ [u]) - val pat_rect1 = flat (map mk_pat - (constructors ~~ constructors' ~~ pat_rect)) - in (pat_rect1, tree) - end) - | SOME (t, i) => raise CASE_ERROR ("Not a datatype constructor: " ^ - Syntax.string_of_term ctxt t, i) - end - | mk _ = raise CASE_ERROR ("Malformed row matrix", ~1) - in mk - end; - -fun case_error s = error ("Error in case expression:\n" ^ s); - -(* Repeated variable occurrences in a pattern are not allowed. *) -fun no_repeat_vars ctxt pat = fold_aterms - (fn x as Free (s, _) => (fn xs => - if member op aconv xs x then - case_error (quote s ^ " occurs repeatedly in the pattern " ^ - quote (Syntax.string_of_term ctxt pat)) - else x :: xs) - | _ => I) pat []; - -fun gen_make_case ty_match ty_inst type_of tab ctxt err used x clauses = - let - fun string_of_clause (pat, rhs) = Syntax.string_of_term ctxt - (Syntax.const "_case1" $ pat $ rhs); - val _ = map (no_repeat_vars ctxt o fst) clauses; - val rows = map_index (fn (i, (pat, rhs)) => - (([], [pat]), (rhs, (i, true)))) clauses; - val rangeT = (case distinct op = (map (type_of o snd) clauses) of - [] => case_error "no clauses given" - | [T] => T - | _ => case_error "all cases must have the same result type"); - val used' = fold add_row_used rows used; - val (patts, case_tm) = mk_case tab ctxt ty_match ty_inst type_of - used' rangeT {path = [x], rows = rows} - handle CASE_ERROR (msg, i) => case_error (msg ^ - (if i < 0 then "" - else "\nIn clause\n" ^ string_of_clause (nth clauses i))); - val patts1 = map - (fn (_, tag, [pat]) => (pat, tag) - | _ => case_error "error in pattern-match translation") patts; - val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1 - val finals = map row_of_pat patts2 - val originals = map (row_of_pat o #2) rows - val _ = case originals \\ finals of - [] => () - | is => (if err then case_error else warning) - ("The following clauses are redundant (covered by preceding clauses):\n" ^ - cat_lines (map (string_of_clause o nth clauses) is)); - in - (case_tm, patts2) - end; - -fun make_case tab ctxt = gen_make_case - (match_type (ProofContext.theory_of ctxt)) Envir.subst_TVars fastype_of tab ctxt; -val make_case_untyped = gen_make_case (K (K Vartab.empty)) - (K (Term.map_types (K dummyT))) (K dummyT); - - -(* parse translation *) - -fun case_tr err tab_of ctxt [t, u] = - let - val thy = ProofContext.theory_of ctxt; - (* replace occurrences of dummy_pattern by distinct variables *) - (* internalize constant names *) - fun prep_pat ((c as Const ("_constrain", _)) $ t $ tT) used = - let val (t', used') = prep_pat t used - in (c $ t' $ tT, used') end - | prep_pat (Const ("dummy_pattern", T)) used = - let val x = Name.variant used "x" - in (Free (x, T), x :: used) end - | prep_pat (Const (s, T)) used = - (case try (unprefix Syntax.constN) s of - SOME c => (Const (c, T), used) - | NONE => (Const (Sign.intern_const thy s, T), used)) - | prep_pat (v as Free (s, T)) used = - let val s' = Sign.intern_const thy s - in - if Sign.declared_const thy s' then - (Const (s', T), used) - else (v, used) - end - | prep_pat (t $ u) used = - let - val (t', used') = prep_pat t used; - val (u', used'') = prep_pat u used' - in - (t' $ u', used'') - end - | prep_pat t used = case_error ("Bad pattern: " ^ Syntax.string_of_term ctxt t); - fun dest_case1 (t as Const ("_case1", _) $ l $ r) = - let val (l', cnstrts) = strip_constraints l - in ((fst (prep_pat l' (Term.add_free_names t [])), r), cnstrts) - end - | dest_case1 t = case_error "dest_case1"; - fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u - | dest_case2 t = [t]; - val (cases, cnstrts) = split_list (map dest_case1 (dest_case2 u)); - val (case_tm, _) = make_case_untyped (tab_of thy) ctxt err [] - (fold (fn tT => fn t => Syntax.const "_constrain" $ t $ tT) - (flat cnstrts) t) cases; - in case_tm end - | case_tr _ _ _ ts = case_error "case_tr"; - - -(*--------------------------------------------------------------------------- - * Pretty printing of nested case expressions - *---------------------------------------------------------------------------*) - -(* destruct one level of pattern matching *) - -fun gen_dest_case name_of type_of tab d used t = - case apfst name_of (strip_comb t) of - (SOME cname, ts as _ :: _) => - let - val (fs, x) = split_last ts; - fun strip_abs i t = - let - val zs = strip_abs_vars t; - val _ = if length zs < i then raise CASE_ERROR ("", 0) else (); - val (xs, ys) = chop i zs; - val u = list_abs (ys, strip_abs_body t); - val xs' = map Free (Name.variant_list (OldTerm.add_term_names (u, used)) - (map fst xs) ~~ map snd xs) - in (xs', subst_bounds (rev xs', u)) end; - fun is_dependent i t = - let val k = length (strip_abs_vars t) - i - in k < 0 orelse exists (fn j => j >= k) - (loose_bnos (strip_abs_body t)) - end; - fun count_cases (_, _, true) = I - | count_cases (c, (_, body), false) = - AList.map_default op aconv (body, []) (cons c); - val is_undefined = name_of #> equal (SOME "HOL.undefined"); - fun mk_case (c, (xs, body), _) = (list_comb (c, xs), body) - in case ty_info tab cname of - SOME {constructors, case_name} => - if length fs = length constructors then - let - val cases = map (fn (Const (s, U), t) => - let - val k = length (binder_types U); - val p as (xs, _) = strip_abs k t - in - (Const (s, map type_of xs ---> type_of x), - p, is_dependent k t) - end) (constructors ~~ fs); - val cases' = sort (int_ord o swap o pairself (length o snd)) - (fold_rev count_cases cases []); - val R = type_of t; - val dummy = if d then Const ("dummy_pattern", R) - else Free (Name.variant used "x", R) - in - SOME (x, map mk_case (case find_first (is_undefined o fst) cases' of - SOME (_, cs) => - if length cs = length constructors then [hd cases] - else filter_out (fn (_, (_, body), _) => is_undefined body) cases - | NONE => case cases' of - [] => cases - | (default, cs) :: _ => - if length cs = 1 then cases - else if length cs = length constructors then - [hd cases, (dummy, ([], default), false)] - else - filter_out (fn (c, _, _) => member op aconv cs c) cases @ - [(dummy, ([], default), false)])) - end handle CASE_ERROR _ => NONE - else NONE - | _ => NONE - end - | _ => NONE; - -val dest_case = gen_dest_case (try (dest_Const #> fst)) fastype_of; -val dest_case' = gen_dest_case - (try (dest_Const #> fst #> unprefix Syntax.constN)) (K dummyT); - - -(* destruct nested patterns *) - -fun strip_case'' dest (pat, rhs) = - case dest (Term.add_free_names pat []) rhs of - SOME (exp as Free _, clauses) => - if member op aconv (OldTerm.term_frees pat) exp andalso - not (exists (fn (_, rhs') => - member op aconv (OldTerm.term_frees rhs') exp) clauses) - then - maps (strip_case'' dest) (map (fn (pat', rhs') => - (subst_free [(exp, pat')] pat, rhs')) clauses) - else [(pat, rhs)] - | _ => [(pat, rhs)]; - -fun gen_strip_case dest t = case dest [] t of - SOME (x, clauses) => - SOME (x, maps (strip_case'' dest) clauses) - | NONE => NONE; - -val strip_case = gen_strip_case oo dest_case; -val strip_case' = gen_strip_case oo dest_case'; - - -(* print translation *) - -fun case_tr' tab_of cname ctxt ts = - let - val thy = ProofContext.theory_of ctxt; - val consts = ProofContext.consts_of ctxt; - fun mk_clause (pat, rhs) = - let val xs = Term.add_frees pat [] - in - Syntax.const "_case1" $ - map_aterms - (fn Free p => Syntax.mark_boundT p - | Const (s, _) => Const (Consts.extern_early consts s, dummyT) - | t => t) pat $ - map_aterms - (fn x as Free (s, T) => - if member (op =) xs (s, T) then Syntax.mark_bound s else x - | t => t) rhs - end - in case strip_case' (tab_of thy) true (list_comb (Syntax.const cname, ts)) of - SOME (x, clauses) => Syntax.const "_case_syntax" $ x $ - foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) - (map mk_clause clauses) - | NONE => raise Match - end; - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_codegen.ML --- a/src/HOL/Tools/datatype_codegen.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,451 +0,0 @@ -(* Title: HOL/Tools/datatype_codegen.ML - Author: Stefan Berghofer and Florian Haftmann, TU Muenchen - -Code generator facilities for inductive datatypes. -*) - -signature DATATYPE_CODEGEN = -sig - val find_shortest_path: DatatypeAux.descr -> int -> (string * int) option - val mk_eq_eqns: theory -> string -> (thm * bool) list - val mk_case_cert: theory -> string -> thm - val setup: theory -> theory -end; - -structure DatatypeCodegen : DATATYPE_CODEGEN = -struct - -(** SML code generator **) - -open Codegen; - -(**** datatype definition ****) - -(* find shortest path to constructor with no recursive arguments *) - -fun find_nonempty (descr: DatatypeAux.descr) is i = - let - val (_, _, constrs) = the (AList.lookup (op =) descr i); - fun arg_nonempty (_, DatatypeAux.DtRec i) = if member (op =) is i - then NONE - else Option.map (curry op + 1 o snd) (find_nonempty descr (i::is) i) - | arg_nonempty _ = SOME 0; - fun max xs = Library.foldl - (fn (NONE, _) => NONE - | (SOME i, SOME j) => SOME (Int.max (i, j)) - | (_, NONE) => NONE) (SOME 0, xs); - val xs = sort (int_ord o pairself snd) - (map_filter (fn (s, dts) => Option.map (pair s) - (max (map (arg_nonempty o DatatypeAux.strip_dtyp) dts))) constrs) - in case xs of [] => NONE | x :: _ => SOME x end; - -fun find_shortest_path descr i = find_nonempty descr [i] i; - -fun add_dt_defs thy defs dep module (descr: DatatypeAux.descr) sorts gr = - let - val descr' = List.filter (can (map DatatypeAux.dest_DtTFree o #2 o snd)) descr; - val rtnames = map (#1 o snd) (List.filter (fn (_, (_, _, cs)) => - exists (exists DatatypeAux.is_rec_type o snd) cs) descr'); - - val (_, (tname, _, _)) :: _ = descr'; - val node_id = tname ^ " (type)"; - val module' = if_library (thyname_of_type thy tname) module; - - fun mk_dtdef prfx [] gr = ([], gr) - | mk_dtdef prfx ((_, (tname, dts, cs))::xs) gr = - let - val tvs = map DatatypeAux.dest_DtTFree dts; - val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs; - val ((_, type_id), gr') = mk_type_id module' tname gr; - val (ps, gr'') = gr' |> - fold_map (fn (cname, cargs) => - fold_map (invoke_tycodegen thy defs node_id module' false) - cargs ##>> - mk_const_id module' cname) cs'; - val (rest, gr''') = mk_dtdef "and " xs gr'' - in - (Pretty.block (str prfx :: - (if null tvs then [] else - [mk_tuple (map str tvs), str " "]) @ - [str (type_id ^ " ="), Pretty.brk 1] @ - List.concat (separate [Pretty.brk 1, str "| "] - (map (fn (ps', (_, cname)) => [Pretty.block - (str cname :: - (if null ps' then [] else - List.concat ([str " of", Pretty.brk 1] :: - separate [str " *", Pretty.brk 1] - (map single ps'))))]) ps))) :: rest, gr''') - end; - - fun mk_constr_term cname Ts T ps = - List.concat (separate [str " $", Pretty.brk 1] - ([str ("Const (\"" ^ cname ^ "\","), Pretty.brk 1, - mk_type false (Ts ---> T), str ")"] :: ps)); - - fun mk_term_of_def gr prfx [] = [] - | mk_term_of_def gr prfx ((_, (tname, dts, cs)) :: xs) = - let - val cs' = map (apsnd (map (DatatypeAux.typ_of_dtyp descr sorts))) cs; - val dts' = map (DatatypeAux.typ_of_dtyp descr sorts) dts; - val T = Type (tname, dts'); - val rest = mk_term_of_def gr "and " xs; - val (eqs, _) = fold_map (fn (cname, Ts) => fn prfx => - let val args = map (fn i => - str ("x" ^ string_of_int i)) (1 upto length Ts) - in (Pretty.blk (4, - [str prfx, mk_term_of gr module' false T, Pretty.brk 1, - if null Ts then str (snd (get_const_id gr cname)) - else parens (Pretty.block - [str (snd (get_const_id gr cname)), - Pretty.brk 1, mk_tuple args]), - str " =", Pretty.brk 1] @ - mk_constr_term cname Ts T - (map2 (fn x => fn U => [Pretty.block [mk_term_of gr module' false U, - Pretty.brk 1, x]]) args Ts)), " | ") - end) cs' prfx - in eqs @ rest end; - - fun mk_gen_of_def gr prfx [] = [] - | mk_gen_of_def gr prfx ((i, (tname, dts, cs)) :: xs) = - let - val tvs = map DatatypeAux.dest_DtTFree dts; - val Us = map (DatatypeAux.typ_of_dtyp descr sorts) dts; - val T = Type (tname, Us); - val (cs1, cs2) = - List.partition (exists DatatypeAux.is_rec_type o snd) cs; - val SOME (cname, _) = find_shortest_path descr i; - - fun mk_delay p = Pretty.block - [str "fn () =>", Pretty.brk 1, p]; - - fun mk_force p = Pretty.block [p, Pretty.brk 1, str "()"]; - - fun mk_constr s b (cname, dts) = - let - val gs = map (fn dt => mk_app false (mk_gen gr module' false rtnames s - (DatatypeAux.typ_of_dtyp descr sorts dt)) - [str (if b andalso DatatypeAux.is_rec_type dt then "0" - else "j")]) dts; - val Ts = map (DatatypeAux.typ_of_dtyp descr sorts) dts; - val xs = map str - (DatatypeProp.indexify_names (replicate (length dts) "x")); - val ts = map str - (DatatypeProp.indexify_names (replicate (length dts) "t")); - val (_, id) = get_const_id gr cname - in - mk_let - (map2 (fn p => fn q => mk_tuple [p, q]) xs ts ~~ gs) - (mk_tuple - [case xs of - _ :: _ :: _ => Pretty.block - [str id, Pretty.brk 1, mk_tuple xs] - | _ => mk_app false (str id) xs, - mk_delay (Pretty.block (mk_constr_term cname Ts T - (map (single o mk_force) ts)))]) - end; - - fun mk_choice [c] = mk_constr "(i-1)" false c - | mk_choice cs = Pretty.block [str "one_of", - Pretty.brk 1, Pretty.blk (1, str "[" :: - List.concat (separate [str ",", Pretty.fbrk] - (map (single o mk_delay o mk_constr "(i-1)" false) cs)) @ - [str "]"]), Pretty.brk 1, str "()"]; - - val gs = maps (fn s => - let val s' = strip_tname s - in [str (s' ^ "G"), str (s' ^ "T")] end) tvs; - val gen_name = "gen_" ^ snd (get_type_id gr tname) - - in - Pretty.blk (4, separate (Pretty.brk 1) - (str (prfx ^ gen_name ^ - (if null cs1 then "" else "'")) :: gs @ - (if null cs1 then [] else [str "i"]) @ - [str "j"]) @ - [str " =", Pretty.brk 1] @ - (if not (null cs1) andalso not (null cs2) - then [str "frequency", Pretty.brk 1, - Pretty.blk (1, [str "[", - mk_tuple [str "i", mk_delay (mk_choice cs1)], - str ",", Pretty.fbrk, - mk_tuple [str "1", mk_delay (mk_choice cs2)], - str "]"]), Pretty.brk 1, str "()"] - else if null cs2 then - [Pretty.block [str "(case", Pretty.brk 1, - str "i", Pretty.brk 1, str "of", - Pretty.brk 1, str "0 =>", Pretty.brk 1, - mk_constr "0" true (cname, valOf (AList.lookup (op =) cs cname)), - Pretty.brk 1, str "| _ =>", Pretty.brk 1, - mk_choice cs1, str ")"]] - else [mk_choice cs2])) :: - (if null cs1 then [] - else [Pretty.blk (4, separate (Pretty.brk 1) - (str ("and " ^ gen_name) :: gs @ [str "i"]) @ - [str " =", Pretty.brk 1] @ - separate (Pretty.brk 1) (str (gen_name ^ "'") :: gs @ - [str "i", str "i"]))]) @ - mk_gen_of_def gr "and " xs - end - - in - (module', (add_edge_acyclic (node_id, dep) gr - handle Graph.CYCLES _ => gr) handle Graph.UNDEF _ => - let - val gr1 = add_edge (node_id, dep) - (new_node (node_id, (NONE, "", "")) gr); - val (dtdef, gr2) = mk_dtdef "datatype " descr' gr1 ; - in - map_node node_id (K (NONE, module', - string_of (Pretty.blk (0, separate Pretty.fbrk dtdef @ - [str ";"])) ^ "\n\n" ^ - (if "term_of" mem !mode then - string_of (Pretty.blk (0, separate Pretty.fbrk - (mk_term_of_def gr2 "fun " descr') @ [str ";"])) ^ "\n\n" - else "") ^ - (if "test" mem !mode then - string_of (Pretty.blk (0, separate Pretty.fbrk - (mk_gen_of_def gr2 "fun " descr') @ [str ";"])) ^ "\n\n" - else ""))) gr2 - end) - end; - - -(**** case expressions ****) - -fun pretty_case thy defs dep module brack constrs (c as Const (_, T)) ts gr = - let val i = length constrs - in if length ts <= i then - invoke_codegen thy defs dep module brack (eta_expand c ts (i+1)) gr - else - let - val ts1 = Library.take (i, ts); - val t :: ts2 = Library.drop (i, ts); - val names = List.foldr OldTerm.add_term_names - (map (fst o fst o dest_Var) (List.foldr OldTerm.add_term_vars [] ts1)) ts1; - val (Ts, dT) = split_last (Library.take (i+1, fst (strip_type T))); - - fun pcase [] [] [] gr = ([], gr) - | pcase ((cname, cargs)::cs) (t::ts) (U::Us) gr = - let - val j = length cargs; - val xs = Name.variant_list names (replicate j "x"); - val Us' = Library.take (j, fst (strip_type U)); - val frees = map Free (xs ~~ Us'); - val (cp, gr0) = invoke_codegen thy defs dep module false - (list_comb (Const (cname, Us' ---> dT), frees)) gr; - val t' = Envir.beta_norm (list_comb (t, frees)); - val (p, gr1) = invoke_codegen thy defs dep module false t' gr0; - val (ps, gr2) = pcase cs ts Us gr1; - in - ([Pretty.block [cp, str " =>", Pretty.brk 1, p]] :: ps, gr2) - end; - - val (ps1, gr1) = pcase constrs ts1 Ts gr ; - val ps = List.concat (separate [Pretty.brk 1, str "| "] ps1); - val (p, gr2) = invoke_codegen thy defs dep module false t gr1; - val (ps2, gr3) = fold_map (invoke_codegen thy defs dep module true) ts2 gr2; - in ((if not (null ts2) andalso brack then parens else I) - (Pretty.block (separate (Pretty.brk 1) - (Pretty.block ([str "(case ", p, str " of", - Pretty.brk 1] @ ps @ [str ")"]) :: ps2))), gr3) - end - end; - - -(**** constructors ****) - -fun pretty_constr thy defs dep module brack args (c as Const (s, T)) ts gr = - let val i = length args - in if i > 1 andalso length ts < i then - invoke_codegen thy defs dep module brack (eta_expand c ts i) gr - else - let - val id = mk_qual_id module (get_const_id gr s); - val (ps, gr') = fold_map - (invoke_codegen thy defs dep module (i = 1)) ts gr; - in (case args of - _ :: _ :: _ => (if brack then parens else I) - (Pretty.block [str id, Pretty.brk 1, mk_tuple ps]) - | _ => (mk_app brack (str id) ps), gr') - end - end; - - -(**** code generators for terms and types ****) - -fun datatype_codegen thy defs dep module brack t gr = (case strip_comb t of - (c as Const (s, T), ts) => - (case DatatypePackage.datatype_of_case thy s of - SOME {index, descr, ...} => - if is_some (get_assoc_code thy (s, T)) then NONE else - SOME (pretty_case thy defs dep module brack - (#3 (the (AList.lookup op = descr index))) c ts gr ) - | NONE => case (DatatypePackage.datatype_of_constr thy s, strip_type T) of - (SOME {index, descr, ...}, (_, U as Type (tyname, _))) => - if is_some (get_assoc_code thy (s, T)) then NONE else - let - val SOME (tyname', _, constrs) = AList.lookup op = descr index; - val SOME args = AList.lookup op = constrs s - in - if tyname <> tyname' then NONE - else SOME (pretty_constr thy defs - dep module brack args c ts (snd (invoke_tycodegen thy defs dep module false U gr))) - end - | _ => NONE) - | _ => NONE); - -fun datatype_tycodegen thy defs dep module brack (Type (s, Ts)) gr = - (case DatatypePackage.get_datatype thy s of - NONE => NONE - | SOME {descr, sorts, ...} => - if is_some (get_assoc_type thy s) then NONE else - let - val (ps, gr') = fold_map - (invoke_tycodegen thy defs dep module false) Ts gr; - val (module', gr'') = add_dt_defs thy defs dep module descr sorts gr' ; - val (tyid, gr''') = mk_type_id module' s gr'' - in SOME (Pretty.block ((if null Ts then [] else - [mk_tuple ps, str " "]) @ - [str (mk_qual_id module tyid)]), gr''') - end) - | datatype_tycodegen _ _ _ _ _ _ _ = NONE; - - -(** generic code generator **) - -(* case certificates *) - -fun mk_case_cert thy tyco = - let - val raw_thms = - (#case_rewrites o DatatypePackage.the_datatype thy) tyco; - val thms as hd_thm :: _ = raw_thms - |> Conjunction.intr_balanced - |> Thm.unvarify - |> Conjunction.elim_balanced (length raw_thms) - |> map Simpdata.mk_meta_eq - |> map Drule.zero_var_indexes - val params = fold_aterms (fn (Free (v, _)) => insert (op =) v - | _ => I) (Thm.prop_of hd_thm) []; - val rhs = hd_thm - |> Thm.prop_of - |> Logic.dest_equals - |> fst - |> Term.strip_comb - |> apsnd (fst o split_last) - |> list_comb; - val lhs = Free (Name.variant params "case", Term.fastype_of rhs); - val asm = (Thm.cterm_of thy o Logic.mk_equals) (lhs, rhs); - in - thms - |> Conjunction.intr_balanced - |> MetaSimplifier.rewrite_rule [(Thm.symmetric o Thm.assume) asm] - |> Thm.implies_intr asm - |> Thm.generalize ([], params) 0 - |> AxClass.unoverload thy - |> Thm.varifyT - end; - - -(* equality *) - -fun mk_eq_eqns thy dtco = - let - val (vs, cos) = DatatypePackage.the_datatype_spec thy dtco; - val { descr, index, inject = inject_thms, ... } = DatatypePackage.the_datatype thy dtco; - val ty = Type (dtco, map TFree vs); - fun mk_eq (t1, t2) = Const (@{const_name eq_class.eq}, ty --> ty --> HOLogic.boolT) - $ t1 $ t2; - fun true_eq t12 = HOLogic.mk_eq (mk_eq t12, HOLogic.true_const); - fun false_eq t12 = HOLogic.mk_eq (mk_eq t12, HOLogic.false_const); - val triv_injects = map_filter - (fn (c, []) => SOME (HOLogic.mk_Trueprop (true_eq (Const (c, ty), Const (c, ty)))) - | _ => NONE) cos; - fun prep_inject (trueprop $ (equiv $ (_ $ t1 $ t2) $ rhs)) = - trueprop $ (equiv $ mk_eq (t1, t2) $ rhs); - val injects = map prep_inject (nth (DatatypeProp.make_injs [descr] vs) index); - fun prep_distinct (trueprop $ (not $ (_ $ t1 $ t2))) = - [trueprop $ false_eq (t1, t2), trueprop $ false_eq (t2, t1)]; - val distincts = maps prep_distinct (snd (nth (DatatypeProp.make_distincts [descr] vs) index)); - val refl = HOLogic.mk_Trueprop (true_eq (Free ("x", ty), Free ("x", ty))); - val simpset = Simplifier.context (ProofContext.init thy) (HOL_basic_ss - addsimps (map Simpdata.mk_eq (@{thm eq} :: @{thm eq_True} :: inject_thms)) - addsimprocs [DatatypePackage.distinct_simproc]); - fun prove prop = Goal.prove_global thy [] [] prop (K (ALLGOALS (simp_tac simpset))) - |> Simpdata.mk_eq; - in map (rpair true o prove) (triv_injects @ injects @ distincts) @ [(prove refl, false)] end; - -fun add_equality vs dtcos thy = - let - fun add_def dtco lthy = - let - val ty = Type (dtco, map TFree vs); - fun mk_side const_name = Const (const_name, ty --> ty --> HOLogic.boolT) - $ Free ("x", ty) $ Free ("y", ty); - val def = HOLogic.mk_Trueprop (HOLogic.mk_eq - (mk_side @{const_name eq_class.eq}, mk_side @{const_name "op ="})); - val def' = Syntax.check_term lthy def; - val ((_, (_, thm)), lthy') = Specification.definition - (NONE, (Attrib.empty_binding, def')) lthy; - val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy); - val thm' = singleton (ProofContext.export lthy' ctxt_thy) thm; - in (thm', lthy') end; - fun tac thms = Class.intro_classes_tac [] - THEN ALLGOALS (ProofContext.fact_tac thms); - fun add_eq_thms dtco thy = - let - val const = AxClass.param_of_inst thy (@{const_name eq_class.eq}, dtco); - val thy_ref = Theory.check_thy thy; - fun mk_thms () = rev ((mk_eq_eqns (Theory.deref thy_ref) dtco)); - in - Code.add_eqnl (const, Lazy.lazy mk_thms) thy - end; - in - thy - |> TheoryTarget.instantiation (dtcos, vs, [HOLogic.class_eq]) - |> fold_map add_def dtcos - |-> (fn def_thms => Class.prove_instantiation_exit_result (map o Morphism.thm) - (fn _ => fn def_thms => tac def_thms) def_thms) - |-> (fn def_thms => fold Code.del_eqn def_thms) - |> fold add_eq_thms dtcos - end; - - -(* liberal addition of code data for datatypes *) - -fun mk_constr_consts thy vs dtco cos = - let - val cs = map (fn (c, tys) => (c, tys ---> Type (dtco, map TFree vs))) cos; - val cs' = map (fn c_ty as (_, ty) => (AxClass.unoverload_const thy c_ty, ty)) cs; - in if is_some (try (Code.constrset_of_consts thy) cs') - then SOME cs - else NONE - end; - -fun add_all_code dtcos thy = - let - val (vs :: _, coss) = (split_list o map (DatatypePackage.the_datatype_spec thy)) dtcos; - val any_css = map2 (mk_constr_consts thy vs) dtcos coss; - val css = if exists is_none any_css then [] - else map_filter I any_css; - val case_rewrites = maps (#case_rewrites o DatatypePackage.the_datatype thy) dtcos; - val certs = map (mk_case_cert thy) dtcos; - in - if null css then thy - else thy - |> fold Code.add_datatype css - |> fold_rev Code.add_default_eqn case_rewrites - |> fold Code.add_case certs - |> add_equality vs dtcos - end; - - - -(** theory setup **) - -val setup = - add_codegen "datatype" datatype_codegen - #> add_tycodegen "datatype" datatype_tycodegen - #> DatatypePackage.interpretation add_all_code - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_package.ML --- a/src/HOL/Tools/datatype_package.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,709 +0,0 @@ -(* Title: HOL/Tools/datatype_package.ML - Author: Stefan Berghofer, TU Muenchen - -Datatype package for Isabelle/HOL. -*) - -signature DATATYPE_PACKAGE = -sig - val quiet_mode : bool ref - val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table - val print_datatypes : theory -> unit - val get_datatype : theory -> string -> DatatypeAux.datatype_info option - val the_datatype : theory -> string -> DatatypeAux.datatype_info - val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option - val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option - val the_datatype_spec : theory -> string -> (string * sort) list * (string * typ list) list - val get_datatype_constrs : theory -> string -> (string * typ) list option - val construction_interpretation : theory - -> {atom : typ -> 'a, dtyp : string -> 'a, rtyp : string * typ list -> 'a list -> 'a} - -> (string * sort) list -> string list - -> (string * (string * 'a list) list) list - * ((string * typ list) * (string * 'a list) list) list - val distinct_simproc : simproc - val make_case : Proof.context -> bool -> string list -> term -> - (term * term) list -> term * (term * (int * bool)) list - val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option - val read_typ: theory -> - (typ list * (string * sort) list) * string -> typ list * (string * sort) list - val interpretation : (string list -> theory -> theory) -> theory -> theory - val rep_datatype : ({distinct : thm list list, - inject : thm list list, - exhaustion : thm list, - rec_thms : thm list, - case_thms : thm list list, - split_thms : (thm * thm) list, - induction : thm, - simps : thm list} -> Proof.context -> Proof.context) -> string list option -> term list - -> theory -> Proof.state; - val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state; - val add_datatype : bool -> bool -> string list -> (string list * binding * mixfix * - (binding * typ list * mixfix) list) list -> theory -> - {distinct : thm list list, - inject : thm list list, - exhaustion : thm list, - rec_thms : thm list, - case_thms : thm list list, - split_thms : (thm * thm) list, - induction : thm, - simps : thm list} * theory - val add_datatype_cmd : bool -> string list -> (string list * binding * mixfix * - (binding * string list * mixfix) list) list -> theory -> - {distinct : thm list list, - inject : thm list list, - exhaustion : thm list, - rec_thms : thm list, - case_thms : thm list list, - split_thms : (thm * thm) list, - induction : thm, - simps : thm list} * theory - val setup: theory -> theory -end; - -structure DatatypePackage : DATATYPE_PACKAGE = -struct - -open DatatypeAux; - -val quiet_mode = quiet_mode; - - -(* theory data *) - -structure DatatypesData = TheoryDataFun -( - type T = - {types: datatype_info Symtab.table, - constrs: datatype_info Symtab.table, - cases: datatype_info Symtab.table}; - - val empty = - {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; - val copy = I; - val extend = I; - fun merge _ - ({types = types1, constrs = constrs1, cases = cases1}, - {types = types2, constrs = constrs2, cases = cases2}) = - {types = Symtab.merge (K true) (types1, types2), - constrs = Symtab.merge (K true) (constrs1, constrs2), - cases = Symtab.merge (K true) (cases1, cases2)}; -); - -val get_datatypes = #types o DatatypesData.get; -val map_datatypes = DatatypesData.map; - -fun print_datatypes thy = - Pretty.writeln (Pretty.strs ("datatypes:" :: - map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy)))); - - -(** theory information about datatypes **) - -fun put_dt_infos (dt_infos : (string * datatype_info) list) = - map_datatypes (fn {types, constrs, cases} => - {types = fold Symtab.update dt_infos types, - constrs = fold Symtab.default (*conservative wrt. overloaded constructors*) - (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst) - (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs, - cases = fold Symtab.update - (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos) - cases}); - -val get_datatype = Symtab.lookup o get_datatypes; - -fun the_datatype thy name = (case get_datatype thy name of - SOME info => info - | NONE => error ("Unknown datatype " ^ quote name)); - -val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get; -val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get; - -fun get_datatype_descr thy dtco = - get_datatype thy dtco - |> Option.map (fn info as { descr, index, ... } => - (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index))); - -fun the_datatype_spec thy dtco = - let - val info as { descr, index, sorts = raw_sorts, ... } = the_datatype thy dtco; - val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index; - val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) - o DatatypeAux.dest_DtTFree) dtys; - val cos = map - (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos; - in (sorts, cos) end; - -fun get_datatype_constrs thy dtco = - case try (the_datatype_spec thy) dtco - of SOME (sorts, cos) => - let - fun subst (v, sort) = TVar ((v, 0), sort); - fun subst_ty (TFree v) = subst v - | subst_ty ty = ty; - val dty = Type (dtco, map subst sorts); - fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty); - in SOME (map mk_co cos) end - | NONE => NONE; - -fun construction_interpretation thy { atom, dtyp, rtyp } sorts tycos = - let - val descr = (#descr o the_datatype thy o hd) tycos; - val k = length tycos; - val descr_of = the o AList.lookup (op =) descr; - val typ_of_dtyp = typ_of_dtyp descr sorts; - fun interpT (dT as DtTFree _) = atom (typ_of_dtyp dT) - | interpT (dT as DtType (tyco, dTs)) = - let - val Ts = map typ_of_dtyp dTs; - in if is_rec_type dT - then rtyp (tyco, Ts) (map interpT dTs) - else atom (Type (tyco, Ts)) - end - | interpT (DtRec l) = if l < k then (dtyp o #1 o descr_of) l - else let - val (tyco, dTs, _) = descr_of l; - val Ts = map typ_of_dtyp dTs; - in rtyp (tyco, Ts) (map interpT dTs) end; - fun interpC (c, dTs) = (c, map interpT dTs); - fun interpD (_, (tyco, _, cs)) = (tyco, map interpC cs); - fun interpR (_, (tyco, dTs, cs)) = ((tyco, map typ_of_dtyp dTs), map interpC cs); - in chop k descr |> (apfst o map) interpD |> (apsnd o map) interpR end; - - - -(** induct method setup **) - -(* case names *) - -local - -fun dt_recs (DtTFree _) = [] - | dt_recs (DtType (_, dts)) = maps dt_recs dts - | dt_recs (DtRec i) = [i]; - -fun dt_cases (descr: descr) (_, args, constrs) = - let - fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i))); - val bnames = map the_bname (distinct (op =) (maps dt_recs args)); - in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end; - - -fun induct_cases descr = - DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr)); - -fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i)); - -in - -fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); - -fun mk_case_names_exhausts descr new = - map (RuleCases.case_names o exhaust_cases descr o #1) - (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); - -end; - -fun add_rules simps case_thms rec_thms inject distinct - weak_case_congs cong_att = - PureThy.add_thmss [((Binding.name "simps", simps), []), - ((Binding.empty, flat case_thms @ - flat distinct @ rec_thms), [Simplifier.simp_add]), - ((Binding.empty, rec_thms), [Code.add_default_eqn_attribute]), - ((Binding.empty, flat inject), [iff_add]), - ((Binding.empty, map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]), - ((Binding.empty, weak_case_congs), [cong_att])] - #> snd; - - -(* add_cases_induct *) - -fun add_cases_induct infos induction thy = - let - val inducts = ProjectRule.projections (ProofContext.init thy) induction; - - fun named_rules (name, {index, exhaustion, ...}: datatype_info) = - [((Binding.empty, nth inducts index), [Induct.induct_type name]), - ((Binding.empty, exhaustion), [Induct.cases_type name])]; - fun unnamed_rule i = - ((Binding.empty, nth inducts i), [Thm.kind_internal, Induct.induct_type ""]); - in - thy |> PureThy.add_thms - (maps named_rules infos @ - map unnamed_rule (length infos upto length inducts - 1)) |> snd - |> PureThy.add_thmss [((Binding.name "inducts", inducts), [])] |> snd - end; - - - -(**** simplification procedure for showing distinctness of constructors ****) - -fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T) - | stripT p = p; - -fun stripC (i, f $ x) = stripC (i + 1, f) - | stripC p = p; - -val distinctN = "constr_distinct"; - -fun distinct_rule thy ss tname eq_t = case #distinct (the_datatype thy tname) of - FewConstrs thms => Goal.prove (Simplifier.the_context ss) [] [] eq_t (K - (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1, - atac 2, resolve_tac thms 1, etac FalseE 1])) - | ManyConstrs (thm, simpset) => - let - val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] = - map (PureThy.get_thm (ThyInfo.the_theory "Datatype" thy)) - ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]; - in - Goal.prove (Simplifier.the_context ss) [] [] eq_t (K - (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1, - full_simp_tac (Simplifier.inherit_context ss simpset) 1, - REPEAT (dresolve_tac [In0_inject, In1_inject] 1), - eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1, - etac FalseE 1])) - end; - -fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) = - (case (stripC (0, t1), stripC (0, t2)) of - ((i, Const (cname1, T1)), (j, Const (cname2, T2))) => - (case (stripT (0, T1), stripT (0, T2)) of - ((i', Type (tname1, _)), (j', Type (tname2, _))) => - if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then - (case (get_datatype_descr thy) tname1 of - SOME (_, (_, constrs)) => let val cnames = map fst constrs - in if cname1 mem cnames andalso cname2 mem cnames then - SOME (distinct_rule thy ss tname1 - (Logic.mk_equals (t, Const ("False", HOLogic.boolT)))) - else NONE - end - | NONE => NONE) - else NONE - | _ => NONE) - | _ => NONE) - | distinct_proc _ _ _ = NONE; - -val distinct_simproc = - Simplifier.simproc @{theory HOL} distinctN ["s = t"] distinct_proc; - -val dist_ss = HOL_ss addsimprocs [distinct_simproc]; - -val simproc_setup = - Simplifier.map_simpset (fn ss => ss addsimprocs [distinct_simproc]); - - -(**** translation rules for case ****) - -fun make_case ctxt = DatatypeCase.make_case - (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt; - -fun strip_case ctxt = DatatypeCase.strip_case - (datatype_of_case (ProofContext.theory_of ctxt)); - -fun add_case_tr' case_names thy = - Sign.add_advanced_trfuns ([], [], - map (fn case_name => - let val case_name' = Sign.const_syntax_name thy case_name - in (case_name', DatatypeCase.case_tr' datatype_of_case case_name') - end) case_names, []) thy; - -val trfun_setup = - Sign.add_advanced_trfuns ([], - [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)], - [], []); - - -(* prepare types *) - -fun read_typ thy ((Ts, sorts), str) = - let - val ctxt = ProofContext.init thy - |> fold (Variable.declare_typ o TFree) sorts; - val T = Syntax.read_typ ctxt str; - in (Ts @ [T], Term.add_tfreesT T sorts) end; - -fun cert_typ sign ((Ts, sorts), raw_T) = - let - val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle - TYPE (msg, _, _) => error msg; - val sorts' = Term.add_tfreesT T sorts; - in (Ts @ [T], - case duplicates (op =) (map fst sorts') of - [] => sorts' - | dups => error ("Inconsistent sort constraints for " ^ commas dups)) - end; - - -(**** make datatype info ****) - -fun make_dt_info alt_names descr sorts induct reccomb_names rec_thms - (((((((((i, (_, (tname, _, _))), case_name), case_thms), - exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) = - (tname, - {index = i, - alt_names = alt_names, - descr = descr, - sorts = sorts, - rec_names = reccomb_names, - rec_rewrites = rec_thms, - case_name = case_name, - case_rewrites = case_thms, - induction = induct, - exhaustion = exhaustion_thm, - distinct = distinct_thm, - inject = inject, - nchotomy = nchotomy, - case_cong = case_cong, - weak_case_cong = weak_case_cong}); - -structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =); -val interpretation = DatatypeInterpretation.interpretation; - - -(******************* definitional introduction of datatypes *******************) - -fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info - case_names_induct case_names_exhausts thy = - let - val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); - - val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |> - DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts - types_syntax constr_syntax case_names_induct; - - val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr - sorts induct case_names_exhausts thy2; - val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms - flat_names new_type_names descr sorts dt_info inject dist_rewrites - (Simplifier.theory_context thy3 dist_ss) induct thy3; - val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms - flat_names new_type_names descr sorts reccomb_names rec_thms thy4; - val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names - descr sorts inject dist_rewrites casedist_thms case_thms thy6; - val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names - descr sorts casedist_thms thy7; - val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names - descr sorts nchotomys case_thms thy8; - val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names - descr sorts thy9; - - val dt_infos = map - (make_dt_info (SOME new_type_names) (flat descr) sorts induct reccomb_names rec_thms) - ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~ - casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); - - val simps = flat (distinct @ inject @ case_thms) @ rec_thms; - - val thy12 = - thy10 - |> add_case_tr' case_names - |> Sign.add_path (space_implode "_" new_type_names) - |> add_rules simps case_thms rec_thms inject distinct - weak_case_congs (Simplifier.attrib (op addcongs)) - |> put_dt_infos dt_infos - |> add_cases_induct dt_infos induct - |> Sign.parent_path - |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd - |> DatatypeInterpretation.data (map fst dt_infos); - in - ({distinct = distinct, - inject = inject, - exhaustion = casedist_thms, - rec_thms = rec_thms, - case_thms = case_thms, - split_thms = split_thms, - induction = induct, - simps = simps}, thy12) - end; - - -(*********************** declare existing type as datatype *********************) - -fun prove_rep_datatype alt_names new_type_names descr sorts induct inject half_distinct thy = - let - val ((_, [induct']), _) = - Variable.importT_thms [induct] (Variable.thm_context induct); - - fun err t = error ("Ill-formed predicate in induction rule: " ^ - Syntax.string_of_term_global thy t); - - fun get_typ (t as _ $ Var (_, Type (tname, Ts))) = - ((tname, map (fst o dest_TFree) Ts) handle TERM _ => err t) - | get_typ t = err t; - val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induct'))); - - val dt_info = get_datatypes thy; - - val distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; - val (case_names_induct, case_names_exhausts) = - (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames)); - - val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); - - val (casedist_thms, thy2) = thy |> - DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induct - case_names_exhausts; - val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms - false new_type_names [descr] sorts dt_info inject distinct - (Simplifier.theory_context thy2 dist_ss) induct thy2; - val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false - new_type_names [descr] sorts reccomb_names rec_thms thy3; - val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms - new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4; - val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names - [descr] sorts casedist_thms thy5; - val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names - [descr] sorts nchotomys case_thms thy6; - val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names - [descr] sorts thy7; - - val ((_, [induct']), thy10) = - thy8 - |> store_thmss "inject" new_type_names inject - ||>> store_thmss "distinct" new_type_names distinct - ||> Sign.add_path (space_implode "_" new_type_names) - ||>> PureThy.add_thms [((Binding.name "induct", induct), [case_names_induct])]; - - val dt_infos = map (make_dt_info alt_names descr sorts induct' reccomb_names rec_thms) - ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~ - map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); - - val simps = flat (distinct @ inject @ case_thms) @ rec_thms; - - val thy11 = - thy10 - |> add_case_tr' case_names - |> add_rules simps case_thms rec_thms inject distinct - weak_case_congs (Simplifier.attrib (op addcongs)) - |> put_dt_infos dt_infos - |> add_cases_induct dt_infos induct' - |> Sign.parent_path - |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) - |> snd - |> DatatypeInterpretation.data (map fst dt_infos); - in - ({distinct = distinct, - inject = inject, - exhaustion = casedist_thms, - rec_thms = rec_thms, - case_thms = case_thms, - split_thms = split_thms, - induction = induct', - simps = simps}, thy11) - end; - -fun gen_rep_datatype prep_term after_qed alt_names raw_ts thy = - let - fun constr_of_term (Const (c, T)) = (c, T) - | constr_of_term t = - error ("Not a constant: " ^ Syntax.string_of_term_global thy t); - fun no_constr (c, T) = error ("Bad constructor: " - ^ Sign.extern_const thy c ^ "::" - ^ Syntax.string_of_typ_global thy T); - fun type_of_constr (cT as (_, T)) = - let - val frees = OldTerm.typ_tfrees T; - val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) T - handle TYPE _ => no_constr cT - val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); - val _ = if length frees <> length vs then no_constr cT else (); - in (tyco, (vs, cT)) end; - - val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); - val _ = case map_filter (fn (tyco, _) => - if Symtab.defined (get_datatypes thy) tyco then SOME tyco else NONE) raw_cs - of [] => () - | tycos => error ("Type(s) " ^ commas (map quote tycos) - ^ " already represented inductivly"); - val raw_vss = maps (map (map snd o fst) o snd) raw_cs; - val ms = case distinct (op =) (map length raw_vss) - of [n] => 0 upto n - 1 - | _ => error ("Different types in given constructors"); - fun inter_sort m = map (fn xs => nth xs m) raw_vss - |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy)) - val sorts = map inter_sort ms; - val vs = Name.names Name.context Name.aT sorts; - - fun norm_constr (raw_vs, (c, T)) = (c, map_atyps - (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); - - val cs = map (apsnd (map norm_constr)) raw_cs; - val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) - o fst o strip_type; - val new_type_names = map Long_Name.base_name (the_default (map fst cs) alt_names); - - fun mk_spec (i, (tyco, constr)) = (i, (tyco, - map (DtTFree o fst) vs, - (map o apsnd) dtyps_of_typ constr)) - val descr = map_index mk_spec cs; - val injs = DatatypeProp.make_injs [descr] vs; - val half_distincts = map snd (DatatypeProp.make_distincts [descr] vs); - val ind = DatatypeProp.make_ind [descr] vs; - val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; - - fun after_qed' raw_thms = - let - val [[[induct]], injs, half_distincts] = - unflat rules (map Drule.zero_var_indexes_list raw_thms); - (*FIXME somehow dubious*) - in - ProofContext.theory_result - (prove_rep_datatype alt_names new_type_names descr vs induct injs half_distincts) - #-> after_qed - end; - in - thy - |> ProofContext.init - |> Proof.theorem_i NONE after_qed' ((map o map) (rpair []) (flat rules)) - end; - -val rep_datatype = gen_rep_datatype Sign.cert_term; -val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global (K I); - - - -(******************************** add datatype ********************************) - -fun gen_add_datatype prep_typ err flat_names new_type_names dts thy = - let - val _ = Theory.requires thy "Datatype" "datatype definitions"; - - (* this theory is used just for parsing *) - - val tmp_thy = thy |> - Theory.copy |> - Sign.add_types (map (fn (tvs, tname, mx, _) => - (tname, length tvs, mx)) dts); - - val (tyvars, _, _, _)::_ = dts; - val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) => - let val full_tname = Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname) - in (case duplicates (op =) tvs of - [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx)) - else error ("Mutually recursive datatypes must have same type parameters") - | dups => error ("Duplicate parameter(s) for datatype " ^ quote (Binding.str_of tname) ^ - " : " ^ commas dups)) - end) dts); - - val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of - [] => () | dups => error ("Duplicate datatypes: " ^ commas dups)); - - fun prep_dt_spec ((tvs, tname, mx, constrs), tname') (dts', constr_syntax, sorts, i) = - let - fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') = - let - val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs); - val _ = (case fold (curry OldTerm.add_typ_tfree_names) cargs' [] \\ tvs of - [] => () - | vs => error ("Extra type variables on rhs: " ^ commas vs)) - in (constrs @ [((if flat_names then Sign.full_name tmp_thy else - Sign.full_name_path tmp_thy tname') - (Binding.map_name (Syntax.const_name mx') cname), - map (dtyp_of_typ new_dts) cargs')], - constr_syntax' @ [(cname, mx')], sorts'') - end handle ERROR msg => cat_error msg - ("The error above occured in constructor " ^ quote (Binding.str_of cname) ^ - " of datatype " ^ quote (Binding.str_of tname)); - - val (constrs', constr_syntax', sorts') = - fold prep_constr constrs ([], [], sorts) - - in - case duplicates (op =) (map fst constrs') of - [] => - (dts' @ [(i, (Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname), - map DtTFree tvs, constrs'))], - constr_syntax @ [constr_syntax'], sorts', i + 1) - | dups => error ("Duplicate constructors " ^ commas dups ^ - " in datatype " ^ quote (Binding.str_of tname)) - end; - - val (dts', constr_syntax, sorts', i) = - fold prep_dt_spec (dts ~~ new_type_names) ([], [], [], 0); - val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts')); - val dt_info = get_datatypes thy; - val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i; - val _ = check_nonempty descr handle (exn as Datatype_Empty s) => - if err then error ("Nonemptiness check failed for datatype " ^ s) - else raise exn; - - val descr' = flat descr; - val case_names_induct = mk_case_names_induct descr'; - val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts); - in - add_datatype_def - flat_names new_type_names descr sorts types_syntax constr_syntax dt_info - case_names_induct case_names_exhausts thy - end; - -val add_datatype = gen_add_datatype cert_typ; -val add_datatype_cmd = gen_add_datatype read_typ true; - - - -(** package setup **) - -(* setup theory *) - -val setup = - DatatypeRepProofs.distinctness_limit_setup #> - simproc_setup #> - trfun_setup #> - DatatypeInterpretation.init; - - -(* outer syntax *) - -local structure P = OuterParse and K = OuterKeyword in - -val datatype_decl = - Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.binding -- P.opt_infix -- - (P.$$$ "=" |-- P.enum1 "|" (P.binding -- Scan.repeat P.typ -- P.opt_mixfix)); - -fun mk_datatype args = - let - val names = map - (fn ((((NONE, _), t), _), _) => Binding.name_of t | ((((SOME t, _), _), _), _) => t) args; - val specs = map (fn ((((_, vs), t), mx), cons) => - (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; - in snd o add_datatype_cmd false names specs end; - -val _ = - OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl - (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); - -val _ = - OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_goal - (Scan.option (P.$$$ "(" |-- Scan.repeat1 P.name --| P.$$$ ")") -- Scan.repeat1 P.term - >> (fn (alt_names, ts) => Toplevel.print - o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts))); - -end; - - -(* document antiquotation *) - -val _ = ThyOutput.antiquotation "datatype" Args.tyname - (fn {source = src, context = ctxt, ...} => fn dtco => - let - val thy = ProofContext.theory_of ctxt; - val (vs, cos) = the_datatype_spec thy dtco; - val ty = Type (dtco, map TFree vs); - fun pretty_typ_bracket (ty as Type (_, _ :: _)) = - Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty] - | pretty_typ_bracket ty = - Syntax.pretty_typ ctxt ty; - fun pretty_constr (co, tys) = - (Pretty.block o Pretty.breaks) - (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) :: - map pretty_typ_bracket tys); - val pretty_datatype = - Pretty.block - (Pretty.command "datatype" :: Pretty.brk 1 :: - Syntax.pretty_typ ctxt ty :: - Pretty.str " =" :: Pretty.brk 1 :: - flat (separate [Pretty.brk 1, Pretty.str "| "] - (map (single o pretty_constr) cos))); - in ThyOutput.output (ThyOutput.maybe_pretty_source (K pretty_datatype) src [()]) end); - -end; - diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_prop.ML --- a/src/HOL/Tools/datatype_prop.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,435 +0,0 @@ -(* Title: HOL/Tools/datatype_prop.ML - Author: Stefan Berghofer, TU Muenchen - -Characteristic properties of datatypes. -*) - -signature DATATYPE_PROP = -sig - val indexify_names: string list -> string list - val make_tnames: typ list -> string list - val make_injs : DatatypeAux.descr list -> (string * sort) list -> term list list - val make_distincts : DatatypeAux.descr list -> - (string * sort) list -> (int * term list) list (*no symmetric inequalities*) - val make_ind : DatatypeAux.descr list -> (string * sort) list -> term - val make_casedists : DatatypeAux.descr list -> (string * sort) list -> term list - val make_primrec_Ts : DatatypeAux.descr list -> (string * sort) list -> - string list -> typ list * typ list - val make_primrecs : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> term list - val make_cases : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> term list list - val make_splits : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> (term * term) list - val make_weak_case_congs : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> term list - val make_case_congs : string list -> DatatypeAux.descr list -> - (string * sort) list -> theory -> term list - val make_nchotomys : DatatypeAux.descr list -> - (string * sort) list -> term list -end; - -structure DatatypeProp : DATATYPE_PROP = -struct - -open DatatypeAux; - -fun indexify_names names = - let - fun index (x :: xs) tab = - (case AList.lookup (op =) tab x of - NONE => if member (op =) xs x then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab - | SOME i => (x ^ string_of_int i) :: index xs ((x, i + 1) :: tab)) - | index [] _ = []; - in index names [] end; - -fun make_tnames Ts = - let - fun type_name (TFree (name, _)) = implode (tl (explode name)) - | type_name (Type (name, _)) = - let val name' = Long_Name.base_name name - in if Syntax.is_identifier name' then name' else "x" end; - in indexify_names (map type_name Ts) end; - - -(************************* injectivity of constructors ************************) - -fun make_injs descr sorts = - let - val descr' = flat descr; - fun make_inj T (cname, cargs) = - if null cargs then I else - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val constr_t = Const (cname, Ts ---> T); - val tnames = make_tnames Ts; - val frees = map Free (tnames ~~ Ts); - val frees' = map Free ((map ((op ^) o (rpair "'")) tnames) ~~ Ts); - in cons (HOLogic.mk_Trueprop (HOLogic.mk_eq - (HOLogic.mk_eq (list_comb (constr_t, frees), list_comb (constr_t, frees')), - foldr1 (HOLogic.mk_binop "op &") - (map HOLogic.mk_eq (frees ~~ frees'))))) - end; - in - map2 (fn d => fn T => fold_rev (make_inj T) (#3 (snd d)) []) - (hd descr) (Library.take (length (hd descr), get_rec_types descr' sorts)) - end; - - -(************************* distinctness of constructors ***********************) - -fun make_distincts descr sorts = - let - val descr' = flat descr; - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - - fun prep_constr (cname, cargs) = (cname, map (typ_of_dtyp descr' sorts) cargs); - - fun make_distincts' _ [] = [] - | make_distincts' T ((cname, cargs)::constrs) = - let - val frees = map Free ((make_tnames cargs) ~~ cargs); - val t = list_comb (Const (cname, cargs ---> T), frees); - - fun make_distincts'' (cname', cargs') = - let - val frees' = map Free ((map ((op ^) o (rpair "'")) - (make_tnames cargs')) ~~ cargs'); - val t' = list_comb (Const (cname', cargs' ---> T), frees') - in - HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t, t')) - end - - in map make_distincts'' constrs @ make_distincts' T constrs end; - - in - map2 (fn ((_, (_, _, constrs))) => fn T => - (length constrs, make_distincts' T (map prep_constr constrs))) (hd descr) newTs - end; - - -(********************************* induction **********************************) - -fun make_ind descr sorts = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val pnames = if length descr' = 1 then ["P"] - else map (fn i => "P" ^ string_of_int i) (1 upto length descr'); - - fun make_pred i T = - let val T' = T --> HOLogic.boolT - in Free (List.nth (pnames, i), T') end; - - fun make_ind_prem k T (cname, cargs) = - let - fun mk_prem ((dt, s), T) = - let val (Us, U) = strip_type T - in list_all (map (pair "x") Us, HOLogic.mk_Trueprop - (make_pred (body_index dt) U $ app_bnds (Free (s, T)) (length Us))) - end; - - val recs = List.filter is_rec_type cargs; - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val recTs' = map (typ_of_dtyp descr' sorts) recs; - val tnames = Name.variant_list pnames (make_tnames Ts); - val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); - val frees = tnames ~~ Ts; - val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); - - in list_all_free (frees, Logic.list_implies (prems, - HOLogic.mk_Trueprop (make_pred k T $ - list_comb (Const (cname, Ts ---> T), map Free frees)))) - end; - - val prems = List.concat (map (fn ((i, (_, _, constrs)), T) => - map (make_ind_prem i T) constrs) (descr' ~~ recTs)); - val tnames = make_tnames recTs; - val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") - (map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T)) - (descr' ~~ recTs ~~ tnames))) - - in Logic.list_implies (prems, concl) end; - -(******************************* case distinction *****************************) - -fun make_casedists descr sorts = - let - val descr' = List.concat descr; - - fun make_casedist_prem T (cname, cargs) = - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val frees = Name.variant_list ["P", "y"] (make_tnames Ts) ~~ Ts; - val free_ts = map Free frees - in list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop - (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))), - HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)))) - end; - - fun make_casedist ((_, (_, _, constrs)), T) = - let val prems = map (make_casedist_prem T) constrs - in Logic.list_implies (prems, HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))) - end - - in map make_casedist - ((hd descr) ~~ Library.take (length (hd descr), get_rec_types descr' sorts)) - end; - -(*************** characteristic equations for primrec combinator **************) - -fun make_primrec_Ts descr sorts used = - let - val descr' = List.concat descr; - - val rec_result_Ts = map TFree (Name.variant_list used (replicate (length descr') "'t") ~~ - replicate (length descr') HOLogic.typeS); - - val reccomb_fn_Ts = List.concat (map (fn (i, (_, _, constrs)) => - map (fn (_, cargs) => - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val recs = List.filter (is_rec_type o fst) (cargs ~~ Ts); - - fun mk_argT (dt, T) = - binder_types T ---> List.nth (rec_result_Ts, body_index dt); - - val argTs = Ts @ map mk_argT recs - in argTs ---> List.nth (rec_result_Ts, i) - end) constrs) descr'); - - in (rec_result_Ts, reccomb_fn_Ts) end; - -fun make_primrecs new_type_names descr sorts thy = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; - - val (rec_result_Ts, reccomb_fn_Ts) = make_primrec_Ts descr sorts used; - - val rec_fns = map (uncurry (mk_Free "f")) - (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts))); - - val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec"; - val reccomb_names = map (Sign.intern_const thy) - (if length descr' = 1 then [big_reccomb_name] else - (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) - (1 upto (length descr')))); - val reccombs = map (fn ((name, T), T') => list_comb - (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns)) - (reccomb_names ~~ recTs ~~ rec_result_Ts); - - fun make_primrec T comb_t ((ts, f::fs), (cname, cargs)) = - let - val recs = List.filter is_rec_type cargs; - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val recTs' = map (typ_of_dtyp descr' sorts) recs; - val tnames = make_tnames Ts; - val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs)); - val frees = map Free (tnames ~~ Ts); - val frees' = map Free (rec_tnames ~~ recTs'); - - fun mk_reccomb ((dt, T), t) = - let val (Us, U) = strip_type T - in list_abs (map (pair "x") Us, - List.nth (reccombs, body_index dt) $ app_bnds t (length Us)) - end; - - val reccombs' = map mk_reccomb (recs ~~ recTs' ~~ frees') - - in (ts @ [HOLogic.mk_Trueprop (HOLogic.mk_eq - (comb_t $ list_comb (Const (cname, Ts ---> T), frees), - list_comb (f, frees @ reccombs')))], fs) - end - - in fst (Library.foldl (fn (x, ((dt, T), comb_t)) => - Library.foldl (make_primrec T comb_t) (x, #3 (snd dt))) - (([], rec_fns), descr' ~~ recTs ~~ reccombs)) - end; - -(****************** make terms of form t_case f1 ... fn *********************) - -fun make_case_combs new_type_names descr sorts thy fname = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val used = List.foldr OldTerm.add_typ_tfree_names [] recTs; - val newTs = Library.take (length (hd descr), recTs); - val T' = TFree (Name.variant used "'t", HOLogic.typeS); - - val case_fn_Ts = map (fn (i, (_, _, constrs)) => - map (fn (_, cargs) => - let val Ts = map (typ_of_dtyp descr' sorts) cargs - in Ts ---> T' end) constrs) (hd descr); - - val case_names = map (fn s => - Sign.intern_const thy (s ^ "_case")) new_type_names - in - map (fn ((name, Ts), T) => list_comb - (Const (name, Ts @ [T] ---> T'), - map (uncurry (mk_Free fname)) (Ts ~~ (1 upto length Ts)))) - (case_names ~~ case_fn_Ts ~~ newTs) - end; - -(**************** characteristic equations for case combinator ****************) - -fun make_cases new_type_names descr sorts thy = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - - fun make_case T comb_t ((cname, cargs), f) = - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val frees = map Free ((make_tnames Ts) ~~ Ts) - in HOLogic.mk_Trueprop (HOLogic.mk_eq - (comb_t $ list_comb (Const (cname, Ts ---> T), frees), - list_comb (f, frees))) - end - - in map (fn (((_, (_, _, constrs)), T), comb_t) => - map (make_case T comb_t) (constrs ~~ (snd (strip_comb comb_t)))) - ((hd descr) ~~ newTs ~~ (make_case_combs new_type_names descr sorts thy "f")) - end; - - -(*************************** the "split" - equations **************************) - -fun make_splits new_type_names descr sorts thy = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val used' = List.foldr OldTerm.add_typ_tfree_names [] recTs; - val newTs = Library.take (length (hd descr), recTs); - val T' = TFree (Name.variant used' "'t", HOLogic.typeS); - val P = Free ("P", T' --> HOLogic.boolT); - - fun make_split (((_, (_, _, constrs)), T), comb_t) = - let - val (_, fs) = strip_comb comb_t; - val used = ["P", "x"] @ (map (fst o dest_Free) fs); - - fun process_constr (((cname, cargs), f), (t1s, t2s)) = - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val frees = map Free (Name.variant_list used (make_tnames Ts) ~~ Ts); - val eqn = HOLogic.mk_eq (Free ("x", T), - list_comb (Const (cname, Ts ---> T), frees)); - val P' = P $ list_comb (f, frees) - in ((List.foldr (fn (Free (s, T), t) => HOLogic.mk_all (s, T, t)) - (HOLogic.imp $ eqn $ P') frees)::t1s, - (List.foldr (fn (Free (s, T), t) => HOLogic.mk_exists (s, T, t)) - (HOLogic.conj $ eqn $ (HOLogic.Not $ P')) frees)::t2s) - end; - - val (t1s, t2s) = List.foldr process_constr ([], []) (constrs ~~ fs); - val lhs = P $ (comb_t $ Free ("x", T)) - in - (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, mk_conj t1s)), - HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ mk_disj t2s))) - end - - in map make_split ((hd descr) ~~ newTs ~~ - (make_case_combs new_type_names descr sorts thy "f")) - end; - -(************************* additional rules for TFL ***************************) - -fun make_weak_case_congs new_type_names descr sorts thy = - let - val case_combs = make_case_combs new_type_names descr sorts thy "f"; - - fun mk_case_cong comb = - let - val Type ("fun", [T, _]) = fastype_of comb; - val M = Free ("M", T); - val M' = Free ("M'", T); - in - Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')), - HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb $ M'))) - end - in - map mk_case_cong case_combs - end; - - -(*--------------------------------------------------------------------------- - * Structure of case congruence theorem looks like this: - * - * (M = M') - * ==> (!!x1,...,xk. (M' = C1 x1..xk) ==> (f1 x1..xk = g1 x1..xk)) - * ==> ... - * ==> (!!x1,...,xj. (M' = Cn x1..xj) ==> (fn x1..xj = gn x1..xj)) - * ==> - * (ty_case f1..fn M = ty_case g1..gn M') - *---------------------------------------------------------------------------*) - -fun make_case_congs new_type_names descr sorts thy = - let - val case_combs = make_case_combs new_type_names descr sorts thy "f"; - val case_combs' = make_case_combs new_type_names descr sorts thy "g"; - - fun mk_case_cong ((comb, comb'), (_, (_, _, constrs))) = - let - val Type ("fun", [T, _]) = fastype_of comb; - val (_, fs) = strip_comb comb; - val (_, gs) = strip_comb comb'; - val used = ["M", "M'"] @ map (fst o dest_Free) (fs @ gs); - val M = Free ("M", T); - val M' = Free ("M'", T); - - fun mk_clause ((f, g), (cname, _)) = - let - val (Ts, _) = strip_type (fastype_of f); - val tnames = Name.variant_list used (make_tnames Ts); - val frees = map Free (tnames ~~ Ts) - in - list_all_free (tnames ~~ Ts, Logic.mk_implies - (HOLogic.mk_Trueprop - (HOLogic.mk_eq (M', list_comb (Const (cname, Ts ---> T), frees))), - HOLogic.mk_Trueprop - (HOLogic.mk_eq (list_comb (f, frees), list_comb (g, frees))))) - end - - in - Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')) :: - map mk_clause (fs ~~ gs ~~ constrs), - HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb' $ M'))) - end - - in - map mk_case_cong (case_combs ~~ case_combs' ~~ hd descr) - end; - -(*--------------------------------------------------------------------------- - * Structure of exhaustion theorem looks like this: - * - * !v. (? y1..yi. v = C1 y1..yi) | ... | (? y1..yj. v = Cn y1..yj) - *---------------------------------------------------------------------------*) - -fun make_nchotomys descr sorts = - let - val descr' = List.concat descr; - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - - fun mk_eqn T (cname, cargs) = - let - val Ts = map (typ_of_dtyp descr' sorts) cargs; - val tnames = Name.variant_list ["v"] (make_tnames Ts); - val frees = tnames ~~ Ts - in - List.foldr (fn ((s, T'), t) => HOLogic.mk_exists (s, T', t)) - (HOLogic.mk_eq (Free ("v", T), - list_comb (Const (cname, Ts ---> T), map Free frees))) frees - end - - in map (fn ((_, (_, _, constrs)), T) => - HOLogic.mk_Trueprop (HOLogic.mk_all ("v", T, mk_disj (map (mk_eqn T) constrs)))) - (hd descr ~~ newTs) - end; - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_realizer.ML --- a/src/HOL/Tools/datatype_realizer.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,230 +0,0 @@ -(* Title: HOL/Tools/datatype_realizer.ML - Author: Stefan Berghofer, TU Muenchen - -Porgram extraction from proofs involving datatypes: -Realizers for induction and case analysis -*) - -signature DATATYPE_REALIZER = -sig - val add_dt_realizers: string list -> theory -> theory - val setup: theory -> theory -end; - -structure DatatypeRealizer : DATATYPE_REALIZER = -struct - -open DatatypeAux; - -fun subsets i j = if i <= j then - let val is = subsets (i+1) j - in map (fn ks => i::ks) is @ is end - else [[]]; - -fun forall_intr_prf (t, prf) = - let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p) - in Abst (a, SOME T, Proofterm.prf_abstract_over t prf) end; - -fun prf_of thm = - Reconstruct.reconstruct_proof (Thm.theory_of_thm thm) (Thm.prop_of thm) (Thm.proof_of thm); - -fun prf_subst_vars inst = - Proofterm.map_proof_terms (subst_vars ([], inst)) I; - -fun is_unit t = snd (strip_type (fastype_of t)) = HOLogic.unitT; - -fun tname_of (Type (s, _)) = s - | tname_of _ = ""; - -fun mk_realizes T = Const ("realizes", T --> HOLogic.boolT --> HOLogic.boolT); - -fun make_ind sorts ({descr, rec_names, rec_rewrites, induction, ...} : datatype_info) is thy = - let - val recTs = get_rec_types descr sorts; - val pnames = if length descr = 1 then ["P"] - else map (fn i => "P" ^ string_of_int i) (1 upto length descr); - - val rec_result_Ts = map (fn ((i, _), P) => - if i mem is then TFree ("'" ^ P, HOLogic.typeS) else HOLogic.unitT) - (descr ~~ pnames); - - fun make_pred i T U r x = - if i mem is then - Free (List.nth (pnames, i), T --> U --> HOLogic.boolT) $ r $ x - else Free (List.nth (pnames, i), U --> HOLogic.boolT) $ x; - - fun mk_all i s T t = - if i mem is then list_all_free ([(s, T)], t) else t; - - val (prems, rec_fns) = split_list (flat (fst (fold_map - (fn ((i, (_, _, constrs)), T) => fold_map (fn (cname, cargs) => fn j => - let - val Ts = map (typ_of_dtyp descr sorts) cargs; - val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts); - val recs = filter (is_rec_type o fst o fst) (cargs ~~ tnames ~~ Ts); - val frees = tnames ~~ Ts; - - fun mk_prems vs [] = - let - val rT = nth (rec_result_Ts) i; - val vs' = filter_out is_unit vs; - val f = mk_Free "f" (map fastype_of vs' ---> rT) j; - val f' = Envir.eta_contract (list_abs_free - (map dest_Free vs, if i mem is then list_comb (f, vs') - else HOLogic.unit)); - in (HOLogic.mk_Trueprop (make_pred i rT T (list_comb (f, vs')) - (list_comb (Const (cname, Ts ---> T), map Free frees))), f') - end - | mk_prems vs (((dt, s), T) :: ds) = - let - val k = body_index dt; - val (Us, U) = strip_type T; - val i = length Us; - val rT = nth (rec_result_Ts) k; - val r = Free ("r" ^ s, Us ---> rT); - val (p, f) = mk_prems (vs @ [r]) ds - in (mk_all k ("r" ^ s) (Us ---> rT) (Logic.mk_implies - (list_all (map (pair "x") Us, HOLogic.mk_Trueprop - (make_pred k rT U (app_bnds r i) - (app_bnds (Free (s, T)) i))), p)), f) - end - - in (apfst (curry list_all_free frees) (mk_prems (map Free frees) recs), j + 1) end) - constrs) (descr ~~ recTs) 1))); - - fun mk_proj j [] t = t - | mk_proj j (i :: is) t = if null is then t else - if (j: int) = i then HOLogic.mk_fst t - else mk_proj j is (HOLogic.mk_snd t); - - val tnames = DatatypeProp.make_tnames recTs; - val fTs = map fastype_of rec_fns; - val ps = map (fn ((((i, _), T), U), s) => Abs ("x", T, make_pred i U T - (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Bound 0) (Bound 0))) - (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names); - val r = if null is then Extraction.nullt else - foldr1 HOLogic.mk_prod (List.mapPartial (fn (((((i, _), T), U), s), tname) => - if i mem is then SOME - (list_comb (Const (s, fTs ---> T --> U), rec_fns) $ Free (tname, T)) - else NONE) (descr ~~ recTs ~~ rec_result_Ts ~~ rec_names ~~ tnames)); - val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &") - (map (fn ((((i, _), T), U), tname) => - make_pred i U T (mk_proj i is r) (Free (tname, T))) - (descr ~~ recTs ~~ rec_result_Ts ~~ tnames))); - val cert = cterm_of thy; - val inst = map (pairself cert) (map head_of (HOLogic.dest_conj - (HOLogic.dest_Trueprop (concl_of induction))) ~~ ps); - - val thm = OldGoals.simple_prove_goal_cterm (cert (Logic.list_implies (prems, concl))) - (fn prems => - [rewrite_goals_tac (map mk_meta_eq [fst_conv, snd_conv]), - rtac (cterm_instantiate inst induction) 1, - ALLGOALS ObjectLogic.atomize_prems_tac, - rewrite_goals_tac (@{thm o_def} :: map mk_meta_eq rec_rewrites), - REPEAT ((resolve_tac prems THEN_ALL_NEW (fn i => - REPEAT (etac allE i) THEN atac i)) 1)]); - - val ind_name = Thm.get_name induction; - val vs = map (fn i => List.nth (pnames, i)) is; - val (thm', thy') = thy - |> Sign.root_path - |> PureThy.store_thm - (Binding.qualified_name (space_implode "_" (ind_name :: vs @ ["correctness"])), thm) - ||> Sign.restore_naming thy; - - val ivs = rev (Term.add_vars (Logic.varify (DatatypeProp.make_ind [descr] sorts)) []); - val rvs = rev (Thm.fold_terms Term.add_vars thm' []); - val ivs1 = map Var (filter_out (fn (_, T) => - tname_of (body_type T) mem ["set", "bool"]) ivs); - val ivs2 = map (fn (ixn, _) => Var (ixn, valOf (AList.lookup (op =) rvs ixn))) ivs; - - val prf = List.foldr forall_intr_prf - (List.foldr (fn ((f, p), prf) => - (case head_of (strip_abs_body f) of - Free (s, T) => - let val T' = Logic.varifyT T - in Abst (s, SOME T', Proofterm.prf_abstract_over - (Var ((s, 0), T')) (AbsP ("H", SOME p, prf))) - end - | _ => AbsP ("H", SOME p, prf))) - (Proofterm.proof_combP - (prf_of thm', map PBound (length prems - 1 downto 0))) (rec_fns ~~ prems_of thm)) ivs2; - - val r' = if null is then r else Logic.varify (List.foldr (uncurry lambda) - r (map Logic.unvarify ivs1 @ filter_out is_unit - (map (head_of o strip_abs_body) rec_fns))); - - in Extraction.add_realizers_i [(ind_name, (vs, r', prf))] thy' end; - - -fun make_casedists sorts ({index, descr, case_name, case_rewrites, exhaustion, ...} : datatype_info) thy = - let - val cert = cterm_of thy; - val rT = TFree ("'P", HOLogic.typeS); - val rT' = TVar (("'P", 0), HOLogic.typeS); - - fun make_casedist_prem T (cname, cargs) = - let - val Ts = map (typ_of_dtyp descr sorts) cargs; - val frees = Name.variant_list ["P", "y"] (DatatypeProp.make_tnames Ts) ~~ Ts; - val free_ts = map Free frees; - val r = Free ("r" ^ Long_Name.base_name cname, Ts ---> rT) - in (r, list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop - (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))), - HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $ - list_comb (r, free_ts))))) - end; - - val SOME (_, _, constrs) = AList.lookup (op =) descr index; - val T = List.nth (get_rec_types descr sorts, index); - val (rs, prems) = split_list (map (make_casedist_prem T) constrs); - val r = Const (case_name, map fastype_of rs ---> T --> rT); - - val y = Var (("y", 0), Logic.legacy_varifyT T); - val y' = Free ("y", T); - - val thm = OldGoals.prove_goalw_cterm [] (cert (Logic.list_implies (prems, - HOLogic.mk_Trueprop (Free ("P", rT --> HOLogic.boolT) $ - list_comb (r, rs @ [y']))))) - (fn prems => - [rtac (cterm_instantiate [(cert y, cert y')] exhaustion) 1, - ALLGOALS (EVERY' - [asm_simp_tac (HOL_basic_ss addsimps case_rewrites), - resolve_tac prems, asm_simp_tac HOL_basic_ss])]); - - val exh_name = Thm.get_name exhaustion; - val (thm', thy') = thy - |> Sign.root_path - |> PureThy.store_thm (Binding.qualified_name (exh_name ^ "_P_correctness"), thm) - ||> Sign.restore_naming thy; - - val P = Var (("P", 0), rT' --> HOLogic.boolT); - val prf = forall_intr_prf (y, forall_intr_prf (P, - List.foldr (fn ((p, r), prf) => - forall_intr_prf (Logic.legacy_varify r, AbsP ("H", SOME (Logic.varify p), - prf))) (Proofterm.proof_combP (prf_of thm', - map PBound (length prems - 1 downto 0))) (prems ~~ rs))); - val r' = Logic.legacy_varify (Abs ("y", Logic.legacy_varifyT T, - list_abs (map dest_Free rs, list_comb (r, - map Bound ((length rs - 1 downto 0) @ [length rs]))))); - - in Extraction.add_realizers_i - [(exh_name, (["P"], r', prf)), - (exh_name, ([], Extraction.nullt, prf_of exhaustion))] thy' - end; - -fun add_dt_realizers names thy = - if ! Proofterm.proofs < 2 then thy - else let - val _ = message "Adding realizers for induction and case analysis ..." - val infos = map (DatatypePackage.the_datatype thy) names; - val info :: _ = infos; - in - thy - |> fold_rev (make_ind (#sorts info) info) (subsets 0 (length (#descr info) - 1)) - |> fold_rev (make_casedists (#sorts info)) infos - end; - -val setup = DatatypePackage.interpretation add_dt_realizers; - -end; diff -r 8d353e3214d0 -r 2b47e8e37c11 src/HOL/Tools/datatype_rep_proofs.ML --- a/src/HOL/Tools/datatype_rep_proofs.ML Wed Jun 10 16:22:54 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,642 +0,0 @@ -(* Title: HOL/Tools/datatype_rep_proofs.ML - Author: Stefan Berghofer, TU Muenchen - -Definitional introduction of datatypes -Proof of characteristic theorems: - - - injectivity of constructors - - distinctness of constructors - - induction theorem -*) - -signature DATATYPE_REP_PROOFS = -sig - val distinctness_limit : int Config.T - val distinctness_limit_setup : theory -> theory - val representation_proofs : bool -> DatatypeAux.datatype_info Symtab.table -> - string list -> DatatypeAux.descr list -> (string * sort) list -> - (binding * mixfix) list -> (binding * mixfix) list list -> attribute - -> theory -> (thm list list * thm list list * thm list list * - DatatypeAux.simproc_dist list * thm) * theory -end; - -structure DatatypeRepProofs : DATATYPE_REP_PROOFS = -struct - -open DatatypeAux; - -(*the kind of distinctiveness axioms depends on number of constructors*) -val (distinctness_limit, distinctness_limit_setup) = - Attrib.config_int "datatype_distinctness_limit" 7; - -val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma); - -val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; - - -(** theory context references **) - -val f_myinv_f = thm "f_myinv_f"; -val myinv_f_f = thm "myinv_f_f"; - - -fun exh_thm_of (dt_info : datatype_info Symtab.table) tname = - #exhaustion (the (Symtab.lookup dt_info tname)); - -(******************************************************************************) - -fun representation_proofs flat_names (dt_info : datatype_info Symtab.table) - new_type_names descr sorts types_syntax constr_syntax case_names_induct thy = - let - val Datatype_thy = ThyInfo.the_theory "Datatype" thy; - val node_name = "Datatype.node"; - val In0_name = "Datatype.In0"; - val In1_name = "Datatype.In1"; - val Scons_name = "Datatype.Scons"; - val Leaf_name = "Datatype.Leaf"; - val Numb_name = "Datatype.Numb"; - val Lim_name = "Datatype.Lim"; - val Suml_name = "Datatype.Suml"; - val Sumr_name = "Datatype.Sumr"; - - val [In0_inject, In1_inject, Scons_inject, Leaf_inject, - In0_eq, In1_eq, In0_not_In1, In1_not_In0, - Lim_inject, Suml_inject, Sumr_inject] = map (PureThy.get_thm Datatype_thy) - ["In0_inject", "In1_inject", "Scons_inject", "Leaf_inject", - "In0_eq", "In1_eq", "In0_not_In1", "In1_not_In0", - "Lim_inject", "Suml_inject", "Sumr_inject"]; - - val descr' = flat descr; - - val big_name = space_implode "_" new_type_names; - val thy1 = add_path flat_names big_name thy; - val big_rec_name = big_name ^ "_rep_set"; - val rep_set_names' = - (if length descr' = 1 then [big_rec_name] else - (map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int) - (1 upto (length descr')))); - val rep_set_names = map (Sign.full_bname thy1) rep_set_names'; - - val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr); - val leafTs' = get_nonrec_types descr' sorts; - val branchTs = get_branching_types descr' sorts; - val branchT = if null branchTs then HOLogic.unitT - else BalancedTree.make (fn (T, U) => Type ("+", [T, U])) branchTs; - val arities = get_arities descr' \ 0; - val unneeded_vars = hd tyvars \\ List.foldr OldTerm.add_typ_tfree_names [] (leafTs' @ branchTs); - val leafTs = leafTs' @ (map (fn n => TFree (n, (the o AList.lookup (op =) sorts) n)) unneeded_vars); - val recTs = get_rec_types descr' sorts; - val newTs = Library.take (length (hd descr), recTs); - val oldTs = Library.drop (length (hd descr), recTs); - val sumT = if null leafTs then HOLogic.unitT - else BalancedTree.make (fn (T, U) => Type ("+", [T, U])) leafTs; - val Univ_elT = HOLogic.mk_setT (Type (node_name, [sumT, branchT])); - val UnivT = HOLogic.mk_setT Univ_elT; - val UnivT' = Univ_elT --> HOLogic.boolT; - val Collect = Const ("Collect", UnivT' --> UnivT); - - val In0 = Const (In0_name, Univ_elT --> Univ_elT); - val In1 = Const (In1_name, Univ_elT --> Univ_elT); - val Leaf = Const (Leaf_name, sumT --> Univ_elT); - val Lim = Const (Lim_name, (branchT --> Univ_elT) --> Univ_elT); - - (* make injections needed for embedding types in leaves *) - - fun mk_inj T' x = - let - fun mk_inj' T n i = - if n = 1 then x else - let val n2 = n div 2; - val Type (_, [T1, T2]) = T - in - if i <= n2 then - Const ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i) - else - Const ("Sum_Type.Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2)) - end - in mk_inj' sumT (length leafTs) (1 + find_index_eq T' leafTs) - end; - - (* make injections for constructors *) - - fun mk_univ_inj ts = BalancedTree.access - {left = fn t => In0 $ t, - right = fn t => In1 $ t, - init = - if ts = [] then Const (@{const_name undefined}, Univ_elT) - else foldr1 (HOLogic.mk_binop Scons_name) ts}; - - (* function spaces *) - - fun mk_fun_inj T' x = - let - fun mk_inj T n i = - if n = 1 then x else - let - val n2 = n div 2; - val Type (_, [T1, T2]) = T; - fun mkT U = (U --> Univ_elT) --> T --> Univ_elT - in - if i <= n2 then Const (Suml_name, mkT T1) $ mk_inj T1 n2 i - else Const (Sumr_name, mkT T2) $ mk_inj T2 (n - n2) (i - n2) - end - in mk_inj branchT (length branchTs) (1 + find_index_eq T' branchTs) - end; - - val mk_lim = List.foldr (fn (T, t) => Lim $ mk_fun_inj T (Abs ("x", T, t))); - - (************** generate introduction rules for representing set **********) - - val _ = message "Constructing representing sets ..."; - - (* make introduction rule for a single constructor *) - - fun make_intr s n (i, (_, cargs)) = - let - fun mk_prem (dt, (j, prems, ts)) = (case strip_dtyp dt of - (dts, DtRec k) => - let - val Ts = map (typ_of_dtyp descr' sorts) dts; - val free_t = - app_bnds (mk_Free "x" (Ts ---> Univ_elT) j) (length Ts) - in (j + 1, list_all (map (pair "x") Ts, - HOLogic.mk_Trueprop - (Free (List.nth (rep_set_names', k), UnivT') $ free_t)) :: prems, - mk_lim free_t Ts :: ts) - end - | _ => - let val T = typ_of_dtyp descr' sorts dt - in (j + 1, prems, (Leaf $ mk_inj T (mk_Free "x" T j))::ts) - end); - - val (_, prems, ts) = List.foldr mk_prem (1, [], []) cargs; - val concl = HOLogic.mk_Trueprop - (Free (s, UnivT') $ mk_univ_inj ts n i) - in Logic.list_implies (prems, concl) - end; - - val intr_ts = maps (fn ((_, (_, _, constrs)), rep_set_name) => - map (make_intr rep_set_name (length constrs)) - ((1 upto (length constrs)) ~~ constrs)) (descr' ~~ rep_set_names'); - - val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy2) = - InductivePackage.add_inductive_global (serial_string ()) - {quiet_mode = ! quiet_mode, verbose = false, kind = Thm.internalK, - alt_name = Binding.name big_rec_name, coind = false, no_elim = true, no_ind = false, - skip_mono = true, fork_mono = false} - (map (fn s => ((Binding.name s, UnivT'), NoSyn)) rep_set_names') [] - (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy1; - - (********************************* typedef ********************************) - - val (typedefs, thy3) = thy2 |> - parent_path flat_names |> - fold_map (fn ((((name, mx), tvs), c), name') => - TypedefPackage.add_typedef false (SOME (Binding.name name')) (name, tvs, mx) - (Collect $ Const (c, UnivT')) NONE - (rtac exI 1 THEN rtac CollectI 1 THEN - QUIET_BREADTH_FIRST (has_fewer_prems 1) - (resolve_tac rep_intrs 1))) - (types_syntax ~~ tyvars ~~ - (Library.take (length newTs, rep_set_names)) ~~ new_type_names) ||> - add_path flat_names big_name; - - (*********************** definition of constructors ***********************) - - val big_rep_name = (space_implode "_" new_type_names) ^ "_Rep_"; - val rep_names = map (curry op ^ "Rep_") new_type_names; - val rep_names' = map (fn i => big_rep_name ^ (string_of_int i)) - (1 upto (length (flat (tl descr)))); - val all_rep_names = map (Sign.intern_const thy3) rep_names @ - map (Sign.full_bname thy3) rep_names'; - - (* isomorphism declarations *) - - val iso_decls = map (fn (T, s) => (Binding.name s, T --> Univ_elT, NoSyn)) - (oldTs ~~ rep_names'); - - (* constructor definitions *) - - fun make_constr_def tname T n ((thy, defs, eqns, i), ((cname, cargs), (cname', mx))) = - let - fun constr_arg (dt, (j, l_args, r_args)) = - let val T = typ_of_dtyp descr' sorts dt; - val free_t = mk_Free "x" T j - in (case (strip_dtyp dt, strip_type T) of - ((_, DtRec m), (Us, U)) => (j + 1, free_t :: l_args, mk_lim - (Const (List.nth (all_rep_names, m), U --> Univ_elT) $ - app_bnds free_t (length Us)) Us :: r_args) - | _ => (j + 1, free_t::l_args, (Leaf $ mk_inj T free_t)::r_args)) - end; - - val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs; - val constrT = (map (typ_of_dtyp descr' sorts) cargs) ---> T; - val abs_name = Sign.intern_const thy ("Abs_" ^ tname); - val rep_name = Sign.intern_const thy ("Rep_" ^ tname); - val lhs = list_comb (Const (cname, constrT), l_args); - val rhs = mk_univ_inj r_args n i; - val def = Logic.mk_equals (lhs, Const (abs_name, Univ_elT --> T) $ rhs); - val def_name = Long_Name.base_name cname ^ "_def"; - val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq - (Const (rep_name, T --> Univ_elT) $ lhs, rhs)); - val ([def_thm], thy') = - thy - |> Sign.add_consts_i [(cname', constrT, mx)] - |> (PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]; - - in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; - - (* constructor definitions for datatype *) - - fun dt_constr_defs ((thy, defs, eqns, rep_congs, dist_lemmas), - ((((_, (_, _, constrs)), tname), T), constr_syntax)) = - let - val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong; - val rep_const = cterm_of thy - (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> Univ_elT)); - val cong' = standard (cterm_instantiate [(cterm_of thy cong_f, rep_const)] arg_cong); - val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma); - val (thy', defs', eqns', _) = Library.foldl ((make_constr_def tname T) (length constrs)) - ((add_path flat_names tname thy, defs, [], 1), constrs ~~ constr_syntax) - in - (parent_path flat_names thy', defs', eqns @ [eqns'], - rep_congs @ [cong'], dist_lemmas @ [dist]) - end; - - val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = Library.foldl dt_constr_defs - ((thy3 |> Sign.add_consts_i iso_decls |> parent_path flat_names, [], [], [], []), - hd descr ~~ new_type_names ~~ newTs ~~ constr_syntax); - - (*********** isomorphisms for new types (introduced by typedef) ***********) - - val _ = message "Proving isomorphism properties ..."; - - val newT_iso_axms = map (fn (_, td) => - (collect_simp (#Abs_inverse td), #Rep_inverse td, - collect_simp (#Rep td))) typedefs; - - val newT_iso_inj_thms = map (fn (_, td) => - (collect_simp (#Abs_inject td) RS iffD1, #Rep_inject td RS iffD1)) typedefs; - - (********* isomorphisms between existing types and "unfolded" types *******) - - (*---------------------------------------------------------------------*) - (* isomorphisms are defined using primrec-combinators: *) - (* generate appropriate functions for instantiating primrec-combinator *) - (* *) - (* e.g. dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *) - (* *) - (* also generate characteristic equations for isomorphisms *) - (* *) - (* e.g. dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *) - (*---------------------------------------------------------------------*) - - fun make_iso_def k ks n ((fs, eqns, i), (cname, cargs)) = - let - val argTs = map (typ_of_dtyp descr' sorts) cargs; - val T = List.nth (recTs, k); - val rep_name = List.nth (all_rep_names, k); - val rep_const = Const (rep_name, T --> Univ_elT); - val constr = Const (cname, argTs ---> T); - - fun process_arg ks' ((i2, i2', ts, Ts), dt) = - let - val T' = typ_of_dtyp descr' sorts dt; - val (Us, U) = strip_type T' - in (case strip_dtyp dt of - (_, DtRec j) => if j mem ks' then - (i2 + 1, i2' + 1, ts @ [mk_lim (app_bnds - (mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us], - Ts @ [Us ---> Univ_elT]) - else - (i2 + 1, i2', ts @ [mk_lim - (Const (List.nth (all_rep_names, j), U --> Univ_elT) $ - app_bnds (mk_Free "x" T' i2) (length Us)) Us], Ts) - | _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (mk_Free "x" T' i2)], Ts)) - end; - - val (i2, i2', ts, Ts) = Library.foldl (process_arg ks) ((1, 1, [], []), cargs); - val xs = map (uncurry (mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); - val ys = map (uncurry (mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); - val f = list_abs_free (map dest_Free (xs @ ys), mk_univ_inj ts n i); - - val (_, _, ts', _) = Library.foldl (process_arg []) ((1, 1, [], []), cargs); - val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq - (rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) - - in (fs @ [f], eqns @ [eqn], i + 1) end; - - (* define isomorphisms for all mutually recursive datatypes in list ds *) - - fun make_iso_defs (ds, (thy, char_thms)) = - let - val ks = map fst ds; - val (_, (tname, _, _)) = hd ds; - val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname); - - fun process_dt ((fs, eqns, isos), (k, (tname, _, constrs))) = - let - val (fs', eqns', _) = Library.foldl (make_iso_def k ks (length constrs)) - ((fs, eqns, 1), constrs); - val iso = (List.nth (recTs, k), List.nth (all_rep_names, k)) - in (fs', eqns', isos @ [iso]) end; - - val (fs, eqns, isos) = Library.foldl process_dt (([], [], []), ds); - val fTs = map fastype_of fs; - val defs = map (fn (rec_name, (T, iso_name)) => (Binding.name (Long_Name.base_name iso_name ^ "_def"), - Logic.mk_equals (Const (iso_name, T --> Univ_elT), - list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos); - val (def_thms, thy') = - apsnd Theory.checkpoint ((PureThy.add_defs false o map Thm.no_attributes) defs thy); - - (* prove characteristic equations *) - - val rewrites = def_thms @ (map mk_meta_eq rec_rewrites); - val char_thms' = map (fn eqn => SkipProof.prove_global thy' [] [] eqn - (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns; - - in (thy', char_thms' @ char_thms) end; - - val (thy5, iso_char_thms) = apfst Theory.checkpoint (List.foldr make_iso_defs - (add_path flat_names big_name thy4, []) (tl descr)); - - (* prove isomorphism properties *) - - fun mk_funs_inv thy thm = - let - val prop = Thm.prop_of thm; - val _ $ (_ $ ((S as Const (_, Type (_, [U, _]))) $ _ )) $ - (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop; - val used = OldTerm.add_term_tfree_names (a, []); - - fun mk_thm i = - let - val Ts = map (TFree o rpair HOLogic.typeS) - (Name.variant_list used (replicate i "'t")); - val f = Free ("f", Ts ---> U) - in SkipProof.prove_global thy [] [] (Logic.mk_implies - (HOLogic.mk_Trueprop (HOLogic.list_all - (map (pair "x") Ts, S $ app_bnds f i)), - HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts, - r $ (a $ app_bnds f i)), f)))) - (fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1), - REPEAT (etac allE 1), rtac thm 1, atac 1]) - end - in map (fn r => r RS subst) (thm :: map mk_thm arities) end; - - (* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *) - - val fun_congs = map (fn T => make_elim (Drule.instantiate' - [SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs; - - fun prove_iso_thms (ds, (inj_thms, elem_thms)) = - let - val (_, (tname, _, _)) = hd ds; - val {induction, ...} = the (Symtab.lookup dt_info tname); - - fun mk_ind_concl (i, _) = - let - val T = List.nth (recTs, i); - val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT); - val rep_set_name = List.nth (rep_set_names, i) - in (HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ - HOLogic.mk_eq (Rep_t $ mk_Free "x" T i, Rep_t $ Bound 0) $ - HOLogic.mk_eq (mk_Free "x" T i, Bound 0)), - Const (rep_set_name, UnivT') $ (Rep_t $ mk_Free "x" T i)) - end; - - val (ind_concl1, ind_concl2) = ListPair.unzip (map mk_ind_concl ds); - - val rewrites = map mk_meta_eq iso_char_thms; - val inj_thms' = map snd newT_iso_inj_thms @ - map (fn r => r RS @{thm injD}) inj_thms; - - val inj_thm = SkipProof.prove_global thy5 [] [] - (HOLogic.mk_Trueprop (mk_conj ind_concl1)) (fn _ => EVERY - [(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, - REPEAT (EVERY - [rtac allI 1, rtac impI 1, - exh_tac (exh_thm_of dt_info) 1, - REPEAT (EVERY - [hyp_subst_tac 1, - rewrite_goals_tac rewrites, - REPEAT (dresolve_tac [In0_inject, In1_inject] 1), - (eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) - ORELSE (EVERY - [REPEAT (eresolve_tac (Scons_inject :: - map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1), - REPEAT (cong_tac 1), rtac refl 1, - REPEAT (atac 1 ORELSE (EVERY - [REPEAT (rtac ext 1), - REPEAT (eresolve_tac (mp :: allE :: - map make_elim (Suml_inject :: Sumr_inject :: - Lim_inject :: inj_thms') @ fun_congs) 1), - atac 1]))])])])]); - - val inj_thms'' = map (fn r => r RS @{thm datatype_injI}) - (split_conj_thm inj_thm); - - val elem_thm = - SkipProof.prove_global thy5 [] [] (HOLogic.mk_Trueprop (mk_conj ind_concl2)) - (fn _ => - EVERY [(indtac induction [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, - rewrite_goals_tac rewrites, - REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW - ((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]); - - in (inj_thms'' @ inj_thms, elem_thms @ (split_conj_thm elem_thm)) - end; - - val (iso_inj_thms_unfolded, iso_elem_thms) = List.foldr prove_iso_thms - ([], map #3 newT_iso_axms) (tl descr); - val iso_inj_thms = map snd newT_iso_inj_thms @ - map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded; - - (* prove dt_rep_set_i x --> x : range dt_Rep_i *) - - fun mk_iso_t (((set_name, iso_name), i), T) = - let val isoT = T --> Univ_elT - in HOLogic.imp $ - (Const (set_name, UnivT') $ mk_Free "x" Univ_elT i) $ - (if i < length newTs then Const ("True", HOLogic.boolT) - else HOLogic.mk_mem (mk_Free "x" Univ_elT i, - Const ("image", [isoT, HOLogic.mk_setT T] ---> UnivT) $ - Const (iso_name, isoT) $ Const (@{const_name UNIV}, HOLogic.mk_setT T))) - end; - - val iso_t = HOLogic.mk_Trueprop (mk_conj (map mk_iso_t - (rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs))); - - (* all the theorems are proved by one single simultaneous induction *) - - val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) - iso_inj_thms_unfolded; - - val iso_thms = if length descr = 1 then [] else - Library.drop (length newTs, split_conj_thm - (SkipProof.prove_global thy5 [] [] iso_t (fn _ => EVERY - [(indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, - REPEAT (rtac TrueI 1), - rewrite_goals_tac (mk_meta_eq choice_eq :: - symmetric (mk_meta_eq @{thm expand_fun_eq}) :: range_eqs), - rewrite_goals_tac (map symmetric range_eqs), - REPEAT (EVERY - [REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @ - maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1), - TRY (hyp_subst_tac 1), - rtac (sym RS range_eqI) 1, - resolve_tac iso_char_thms 1])]))); - - val Abs_inverse_thms' = - map #1 newT_iso_axms @ - map2 (fn r_inj => fn r => f_myinv_f OF [r_inj, r RS mp]) - iso_inj_thms_unfolded iso_thms; - - val Abs_inverse_thms = maps (mk_funs_inv thy5) Abs_inverse_thms'; - - (******************* freeness theorems for constructors *******************) - - val _ = message "Proving freeness of constructors ..."; - - (* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) - - fun prove_constr_rep_thm eqn = - let - val inj_thms = map fst newT_iso_inj_thms; - val rewrites = @{thm o_def} :: constr_defs @ (map (mk_meta_eq o #2) newT_iso_axms) - in SkipProof.prove_global thy5 [] [] eqn (fn _ => EVERY - [resolve_tac inj_thms 1, - rewrite_goals_tac rewrites, - rtac refl 3, - resolve_tac rep_intrs 2, - REPEAT (resolve_tac iso_elem_thms 1)]) - end; - - (*--------------------------------------------------------------*) - (* constr_rep_thms and rep_congs are used to prove distinctness *) - (* of constructors. *) - (*--------------------------------------------------------------*) - - val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; - - val dist_rewrites = map (fn (rep_thms, dist_lemma) => - dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) - (constr_rep_thms ~~ dist_lemmas); - - fun prove_distinct_thms _ _ (_, []) = [] - | prove_distinct_thms lim dist_rewrites' (k, ts as _ :: _) = - if k >= lim then [] else let - (*number of constructors < distinctness_limit : C_i ... ~= C_j ...*) - fun prove [] = [] - | prove (t :: ts) = - let - val dist_thm = SkipProof.prove_global thy5 [] [] t (fn _ => - EVERY [simp_tac (HOL_ss addsimps dist_rewrites') 1]) - in dist_thm :: standard (dist_thm RS not_sym) :: prove ts end; - in prove ts end; - - val distinct_thms = DatatypeProp.make_distincts descr sorts - |> map2 (prove_distinct_thms - (Config.get_thy thy5 distinctness_limit)) dist_rewrites; - - val simproc_dists = map (fn ((((_, (_, _, constrs)), rep_thms), congr), dists) => - if length constrs < Config.get_thy thy5 distinctness_limit - then FewConstrs dists - else ManyConstrs (congr, HOL_basic_ss addsimps rep_thms)) (hd descr ~~ - constr_rep_thms ~~ rep_congs ~~ distinct_thms); - - (* prove injectivity of constructors *) - - fun prove_constr_inj_thm rep_thms t = - let val inj_thms = Scons_inject :: (map make_elim - (iso_inj_thms @ - [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, - Lim_inject, Suml_inject, Sumr_inject])) - in SkipProof.prove_global thy5 [] [] t (fn _ => EVERY - [rtac iffI 1, - REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2, - dresolve_tac rep_congs 1, dtac box_equals 1, - REPEAT (resolve_tac rep_thms 1), - REPEAT (eresolve_tac inj_thms 1), - REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1), - REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1), - atac 1]))]) - end; - - val constr_inject = map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) - ((DatatypeProp.make_injs descr sorts) ~~ constr_rep_thms); - - val ((constr_inject', distinct_thms'), thy6) = - thy5 - |> parent_path flat_names - |> store_thmss "inject" new_type_names constr_inject - ||>> store_thmss "distinct" new_type_names distinct_thms; - - (*************************** induction theorem ****************************) - - val _ = message "Proving induction rule for datatypes ..."; - - val Rep_inverse_thms = (map (fn (_, iso, _) => iso RS subst) newT_iso_axms) @ - (map (fn r => r RS myinv_f_f RS subst) iso_inj_thms_unfolded); - val Rep_inverse_thms' = map (fn r => r RS myinv_f_f) iso_inj_thms_unfolded; - - fun mk_indrule_lemma ((prems, concls), ((i, _), T)) = - let - val Rep_t = Const (List.nth (all_rep_names, i), T --> Univ_elT) $ - mk_Free "x" T i; - - val Abs_t = if i < length newTs then - Const (Sign.intern_const thy6 - ("Abs_" ^ (List.nth (new_type_names, i))), Univ_elT --> T) - else Const ("Inductive.myinv", [T --> Univ_elT, Univ_elT] ---> T) $ - Const (List.nth (all_rep_names, i), T --> Univ_elT) - - in (prems @ [HOLogic.imp $ - (Const (List.nth (rep_set_names, i), UnivT') $ Rep_t) $ - (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], - concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i]) - end; - - val (indrule_lemma_prems, indrule_lemma_concls) = - Library.foldl mk_indrule_lemma (([], []), (descr' ~~ recTs)); - - val cert = cterm_of thy6; - - val indrule_lemma = SkipProof.prove_global thy6 [] [] - (Logic.mk_implies - (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems), - HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY - [REPEAT (etac conjE 1), - REPEAT (EVERY - [TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1, - etac mp 1, resolve_tac iso_elem_thms 1])]); - - val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); - val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else - map (Free o apfst fst o dest_Var) Ps; - val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma; - - val dt_induct_prop = DatatypeProp.make_ind descr sorts; - val dt_induct = SkipProof.prove_global thy6 [] - (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) - (fn {prems, ...} => EVERY - [rtac indrule_lemma' 1, - (indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1, - EVERY (map (fn (prem, r) => (EVERY - [REPEAT (eresolve_tac Abs_inverse_thms 1), - simp_tac (HOL_basic_ss addsimps ((symmetric r)::Rep_inverse_thms')) 1, - DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) - (prems ~~ (constr_defs @ (map mk_meta_eq iso_char_thms))))]); - - val ([dt_induct'], thy7) = - thy6 - |> Sign.add_path big_name - |> PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] - ||> Sign.parent_path - ||> Theory.checkpoint; - - in - ((constr_inject', distinct_thms', dist_rewrites, simproc_dists, dt_induct'), thy7) - end; - -end;